Why do MY animations play on THEIR character too?

I have a script that plays animations on the client, and fires a remote event to play them on the server as well. However, when my animations are played, they are also played every other players character on my screen, as though something is telling ALL characters to play this animation. Does anyone know what could be causing this? Thank you tons in advance.

(Rather than someone combing through like 300 lines, I was hoping someone could suggest a possible issue to look for? Could it be something to do with the remote events which are stored plainly in replicatedstorage?)

local Pawn = game:GetService("Players").LocalPlayer 
    local mouse = Pawn:GetMouse()
        local character = Pawn.Character
            if not character or not character.Parent then
             character = Pawn.CharacterAdded:wait()
                end
    local Anim = Instance.new("Animation")
        local grounded = false
            local already_ran = false 
---------------Assets and Events----------
local Idle =("rbxassetid://661054611")
local Walk = ("rbxassetid://661645004")
local CombatIdle =("rbxassetid://658368358")
local CombatWalk = ("rbxassetid://658801474")
local CombatSprint = ("rbxassetid://671718470")
local DodgeBack = ("rbxassetid://671817732")
local Sprint = ("rbxassetid://662016268") 
local Left_Swing = ("rbxassetid://662302773")
local Left_Swing2 = ("rbxassetid://671753749")
local Right_Swing = ("rbxassetid://662302773")
local Central_Swing = ("rbxassetid://672013731")
local Central_Swing2 = ("rbxassetid://672013731")
local Sheathe = ("rbxassetid://664055993")
local Unsheathe = ("rbxassetid://664054478")
local Walkspeed = 14
local SprintEvent = game.ReplicatedStorage:WaitForChild("SprintEvent")
local SheatheEvent = game.ReplicatedStorage:WaitForChild("SheatheEvent")
local UnSheatheEvent = game.ReplicatedStorage:WaitForChild("UnSheatheEvent")
local DodgeEvent = game.ReplicatedStorage:WaitForChild("DodgeEvent")
local FootSmoke = game.ReplicatedStorage:WaitForChild("FootSmoke")
local Animate = game.ReplicatedStorage:WaitForChild("AnimateEvent")
-----------Global Functions-----------
function PlayAnim(parent)
    local AnimTrack = character.Humanoid:LoadAnimation(Anim)
          for _,anim in pairs(character.Humanoid:GetPlayingAnimationTracks()) do
                anim:Stop()
            break
                end
                    wait(.01)
                        AnimTrack:Play()
                            AnimTrack:AdjustSpeed(1)
                                end
function PlayAnim2(parent)
    local AnimTrack = character.Humanoid:LoadAnimation(Anim)
                        AnimTrack:Play()
                            AnimTrack:AdjustSpeed(1)
                                end

function ChangeStance(Value)
script.CombatStance.Value = Value
end
---------------Movement Functionality-----------------------

            function onGround(speed)
                if grounded == false then
                    print("Grounded")
                    grounded = true
                    end

                if speed > 1 and script.CombatStance.Value == ("Explorative") and script.Sprinting.Value == false then
                if already_ran == false then
                already_ran = true
                Anim.AnimationId = (Walk)
                PlayAnim(Anim)
                Animate:FireServer(Walk) 
                print("Runnin!")

                    end

                elseif  speed > 1 and script.CombatStance.Value == ("Combative") and script.Sprinting.Value == false then
                    if already_ran == false then
                        already_ran = true
                        Anim.AnimationId = (CombatWalk)
                        PlayAnim(Anim)
                        Animate:FireServer(CombatWalk) 
                        FootSmoke:FireServer(false)
                    end 

                elseif speed > 1 and script.CombatStance.Value == ("Explorative") and script.Sprinting.Value == true  then
                    if already_ran == false then
                        already_ran = true
                        Anim.AnimationId = (Sprint)
                        PlayAnim(Anim)
                        Animate:FireServer(Sprint) 
                        FootSmoke:FireServer(true)
                    end


                elseif speed > 0 and already_ran == true and script.CombatStance.Value == ("Explorative")  then
                    already_ran = false
                    Anim.AnimationId = (Idle)
                    PlayAnim(Anim)
                    Animate:FireServer(Idle) 
                    FootSmoke:FireServer(false)

                elseif speed > 0 and already_ran == true and script.CombatStance.Value == ("Combative")  then
                    already_ran = false
                    Anim.AnimationId = (CombatIdle)
                    Animate:FireServer(CombatIdle) 
                    PlayAnim(Anim)

                    end
                    end

    character.Humanoid.Running:connect(onGround)
---------------------Input Events------------------------

function onKeyPress(inputObject, gameProcessedEvent)

    if inputObject.KeyCode == Enum.KeyCode.LeftShift and script.Sprinting.Value == (false) and script.CombatStance.Value == ("Explorative") then
        script.Sprinting.Value = (true)
        Walkspeed = 36
        SprintEvent:FireServer(Walkspeed)

        elseif inputObject.KeyCode == Enum.KeyCode.LeftShift and script.Sprinting.Value == (true) then
        script.Sprinting.Value = (false)
        Walkspeed = 20
        SprintEvent:FireServer(Walkspeed)

        elseif inputObject.KeyCode == Enum.KeyCode.C and script.CombatStance.Value == ("Explorative") then
                script.CombatStance.Value = ("Combative")
                    Anim.AnimationId = (Unsheathe)
                    PlayAnim(Anim)
                    Animate:FireServer(Unsheathe)
                    UnSheatheEvent:FireServer(0)
            wait(1)
                Walkspeed = 20
                script.Sprinting.Value = false
                    SprintEvent:FireServer(Walkspeed)
                    Animate:FireServer(CombatIdle)
                    Anim.AnimationId = (CombatIdle)
                    PlayAnim(Anim)

        elseif inputObject.KeyCode == Enum.KeyCode.C and script.CombatStance.Value == ("Combative") then
                script.CombatStance.Value = ("Explorative")
                    Anim.AnimationId = (Sheathe)
                    PlayAnim(Anim)
                    Animate:FireServer(Sheathe)
                    SheatheEvent:FireServer(0)
                wait(1)
                    SprintEvent:FireServer(Walkspeed)
                    Anim.AnimationId = (Idle)
                    PlayAnim(Anim)
                    Animate:FireServer(Idle)

        elseif inputObject.KeyCode == Enum.KeyCode.T and script.CombatStance.Value == ("Combative") then
                script.CombatStance.Value = ("Tools")
                    Anim.AnimationId = (Sheathe)
                    PlayAnim(Anim)
                    Animate:FireServer(Sheathe)
                    SheatheEvent:FireServer(0)
                wait(1)
                    SprintEvent:FireServer(Walkspeed)
                    Anim.AnimationId = (Idle)
                    PlayAnim(Anim)
                    Animate:FireServer(Idle)

        elseif inputObject.KeyCode == Enum.KeyCode.R and script.CombatStance.Value == ("Combative") then
                Anim.AnimationId = (DodgeBack)
                PlayAnim(Anim)
                Animate:FireServer(DodgeBack)
                DodgeEvent:FireServer(0)
                wait(0.7)
                SprintEvent:FireServer(Walkspeed)
                Anim.AnimationId = (CombatIdle)
                Animate:FireServer(CombatIdle)
                PlayAnim(Anim)

        elseif inputObject.KeyCode == Enum.KeyCode.F  then
            script.SwingDirection.Value = ("Left")
                script.AttackCoolDown.Value = (0)
        elseif inputObject.KeyCode == Enum.KeyCode.G  then
            script.SwingDirection.Value = ("Central")
                script.AttackCoolDown.Value = (0)
        elseif inputObject.KeyCode == Enum.KeyCode.H  then
            script.SwingDirection.Value = ("Right")
                script.AttackCoolDown.Value = (0)
    end
end 

game:GetService("UserInputService").InputBegan:connect(onKeyPress)



mouse.Button1Down:connect(function()
if script.CombatStance.Value == ("Combative") and script.SwingVariant.Value == ("First") and script.SwingDirection.Value == ("Left") and script.AttackCoolDown.Value == (0) then
    script.SwingVariant.Value = ("Second")
        script.AttackCoolDown.Value = 2
            Anim.AnimationId = (Left_Swing)
            PlayAnim2(Anim)
            Animate:FireServer(Left_Swing)
            print("Attacking")
            wait(1)
            script.AttackCoolDown.Value = 0

    elseif script.CombatStance.Value == ("Combative") and script.SwingVariant.Value == ("Second") and script.SwingDirection.Value == ("Left") and script.AttackCoolDown.Value == (0) then
    script.SwingVariant.Value = ("First")
        script.AttackCoolDown.Value = 2
            Anim.AnimationId = (Left_Swing2)
            Animate:FireServer(Left_Swing2)
            PlayAnim2(Anim)
            print("Attacking")
            wait(1)
            script.AttackCoolDown.Value = 0

    elseif script.CombatStance.Value == ("Combative") and script.SwingVariant.Value == ("First") and script.SwingDirection.Value == ("Central") and script.AttackCoolDown.Value == (0) then
    script.SwingVariant.Value = ("Second")
        script.AttackCoolDown.Value = 2
            Anim.AnimationId = (Central_Swing)
            Animate:FireServer(Central_Swing)
            PlayAnim2(Anim)
        print("Attacking")
        wait(1)
        script.AttackCoolDown.Value = 0

    elseif script.CombatStance.Value == ("Combative") and script.SwingVariant.Value == ("Second") and script.SwingDirection.Value == ("Central") and script.AttackCoolDown.Value == (0) then
        script.SwingVariant.Value = ("First")
            script.AttackCoolDown.Value = 2
            Anim.AnimationId = (Central_Swing2)
            Animate:FireServer(Central_Swing2)
            PlayAnim2(Anim)
            print("Attacking")
            wait(1)
            script.AttackCoolDown.Value = 0
    end
end)

--SERVER STUFF
local Pawn = script.Parent
local Anim = Instance.new("Animation")

function playAnimation(parent)
        local AnimTrack = Pawn.Humanoid:LoadAnimation(Anim)
        AnimTrack:Stop()
        wait(.01)
        AnimTrack:Play()
        AnimTrack:AdjustSpeed(1)
end

Animate.OnServerEvent:connect(function(player,AnimationStyle) -- OnServerEvent automatically passes the player who fired it as the first argument.   



            for _,anim in pairs(Pawn.Humanoid:GetPlayingAnimationTracks()) do
                anim:Stop()
            break
            end

                Anim.AnimationId = (AnimationStyle)
                playAnimation(Anim)


            end)