This code is messy and complicated. That hides a lot of issues. You have to clean it up first!

First: tab your code correctly. It makes it immensely easier to understand.

Second: pull functions out to where they belong. Functions defined inside of functions (or loops, as it were also) are only desirable when you actually need it. I'm talking about reloadGun, and Button1Up.

Third: eliminate == false and == true. It's harder to read -- just use if thing and if not thing. It's also wrong in the case of FindFirstChild -- FindFirstChild produces nil, not false when the object doesn't exist.

Fourth: separate your constants (reloadtime) from your variables (ammo). I suggest naming your constants IN_ALL_UPPERCASE to distinguish them. reload isn't used.

Fifth: remove and move unnecessary definitions. main isn't used anywhere. user is only used inside the Equipped event, so define it there, not outside. auto, too.

Another problem is that you are repeatedly binding to the ContextActionService. You only should do that once -- and it should be done separately from everything else. It has no business being nested into the Button1Down event.

Here's what I have at this point (one bug fixed, much cleaner, two problematic things removed... so far):

--[[SETTINGS]]--

DAMAGE = 30 -- Set this to how much damage you want the gun to do
RPM = 600 -- How many rounds a minute can the gun fire?
FIRING_RATE = 60 / RPM
RELOAD_TIME = 2 -- Set this to how long you want to take to reload

--[[SETTINGS/]]--

ammo = 10 -- How much ammo in a clip do you want?
ammostore = 100 -- How many stored rounds do you want?

-- <WELD STUFF>

local tool = script.Parent

reloading = false

function reloadGun(name, state, input)
    if state == Enum.UserInputState.Begin then
        print("key has been pressed")
        if ammo < 10 and ammostore > 10 then
            reloading = true
            local difference = ammo - 10
            ammo = ammo + difference
            print(ammo .. " " .. difference)
            ammostore = ammostore - difference
            print(ammostore)
            wait(RELOAD_TIME)
            reloading = false
        else
            print("No ammo left! Da fuzz home boi! Da fuzz")
        end
    end
end
-- Listen for reload action
local CAS = game:GetService("ContextActionService")
CAS:BindAction("ReloadGun", reloadGun, true, Enum.KeyCode.R, Enum.KeyCode.ButtonX)

local canfire = true
tool.Equipped:connect(function(mouse)
    print("Equipped")
    local user = tool.Parent
    if not script.Parent:FindFirstChild("ammo") then
        print("There ain't no ammo vals! better make 'ne")
        local a = Instance.new("NumberValue", script.Parent)
        a.Name = "ammo"
        a.Value = ammo
        local b = Instance.new("NumberValue", script.Parent)
        b.Name = "storedammo"
        b.Value = ammostore
    end
    local auto = false
    mouse.Button1Up:connect(function()
        print("Button is up")
        auto = false
    end)
    mouse.Button1Down:connect(function()
        print("I should fire now")
        auto = true
        while auto do
            print("I can fire now")
            if not canfire and not reloading then return end
            print("I love donkeys")
            canfire = false
            if ammo > 0 then
                ammo = ammo - 1
                print(ammo .. " shots left")

                -- Mah first ray evar
                local ray = Ray.new(tool.Handle.CFrame.p, (mouse.Hit.p -  tool.Handle.CFrame.p).unit*300)
                local hit, position = game.Workspace:FindPartOnRay(ray, user)
                print(position)
                print(ammo .. " shots left")

                print(hit) -- This is used for debugging
                local hitted = hit and hit.Parent and hit.Parent:FindFirstChild("Humanoid")

                if hitted then
                    hitted:TakeDamage(DAMAGE)
                    wait(FIRING_RATE)
                    canfire = true
                else
                    print("You have no ammo.")
                end
            end
        end
    end)
end)

Problems

This line looks wrong:

if not canfire and not reloading then return end

You should probably continue if not reloading, not give up. Of course, it seems like it makes more sense to just add these to the while.

The else for if hitted then is completely off. You have ammo -- you just didn't hit a person. canfire should be set whether or not you hit someone. Similarly, the wait has to be out of the if.

canfire, though, is only necessary to prevent multiple loops from happening at the same time. The waits already stop this one. Why not just stop the loop from happening in the first place if there's already one going on -- which you know from auto?

Technically, auto needs to be a bit stronger because of the delay before checking mouse up. You could use a local variable and connect the MouseUp inside (but remember to disconnect it!) or you can use an identifier to know this is the right loop. Here's what I have now:

-- <weld stuff before me>
local tool = script.Parent

reloading = false

function reloadGun(name, state, input)
    if state == Enum.UserInputState.Begin then
        print("key has been pressed")
        if ammo < 10 and ammostore > 10 then
            reloading = true
            local difference = ammo - 10
            ammo = ammo + difference
            print(ammo .. " " .. difference)
            ammostore = ammostore - difference
            print(ammostore)
            wait(RELOAD_TIME)
            reloading = false
        else
            print("No ammo left! Da fuzz home boi! Da fuzz")
        end
    end
end
-- Listen for reload action
local CAS = game:GetService("ContextActionService")
CAS:BindAction("ReloadGun", reloadGun, true, Enum.KeyCode.R, Enum.KeyCode.ButtonX)

local firing = false
tool.Equipped:connect(function(mouse)
    print("Equipped")
    local user = tool.Parent
    if not script.Parent:FindFirstChild("ammo") then
        print("There ain't no ammo vals! better make 'ne")
        local a = Instance.new("NumberValue", script.Parent)
        a.Name = "ammo"
        a.Value = ammo
        local b = Instance.new("NumberValue", script.Parent)
        b.Name = "storedammo"
        b.Value = ammostore
    end
    mouse.Button1Up:connect(function()
        print("Button is up")
        firing = false
    end)
    mouse.Button1Down:connect(function()
        if firing then
            return -- The mouse is already down, and a loop is still running
        end
        local me = {}
        firing = me
        while firing == me and not reloading and ammo > 0 do
            -- Stop if reloading or someone else is firing, or I run out of ammo
            ammo = ammo - 1
            print(ammo .. " shots left")

            local ray = Ray.new(tool.Handle.CFrame.p, (mouse.Hit.p -  tool.Handle.CFrame.p).unit*300)
            local hit, position = game.Workspace:FindPartOnRay(ray, user)
            print(position)

            print(hit) -- This is used for debugging
            local hitted = hit and hit.Parent and hit.Parent:FindFirstChild("Humanoid")
            if hitted then
                hitted:TakeDamage(DAMAGE)
            end
            wait(FIRING_RATE)
        end
    end)
end)

reloadGun doesn't look right. If you just want to move ammostore into ammo, do that:

            ammo = ammo + ammostore
            ammostore = 0

If you only want to move MAX_AMMO, then that just looks like this:

             -- move the lesser of what you have and what you want
            local move = math.min(ammostore, MAX_AMMO)
            ammo = ammo + move
            ammostore = ammostore - move

Finished Clean Up

--[[SETTINGS]]--

DAMAGE = 30 -- Set this to how much damage you want the gun to do
RPM = 600 -- How many rounds a minute can the gun fire?
FIRING_RATE = 60 / RPM
RELOAD_TIME = 2 -- Set this to how long you want to take to reload
MAX_AMMO = 10
--[[SETTINGS/]]--

ammo = MAX_AMMO -- How much ammo in a clip do you want?
ammostore = 100 -- How many stored rounds do you want?

-- <WELD STUFF>

local tool = script.Parent

reloading = false

function reloadGun(name, state, input)
    if state == Enum.UserInputState.Begin then
        print("reload key has been pressed")
        if ammostore > 0 then
            reloading = true
             -- move the lesser of what you have and what you want
            local move = math.min(ammostore, MAX_AMMO)
            ammo = ammo + move
            ammostore = ammostore - move
            wait(RELOAD_TIME)
            reloading = false
        end
    end
end
-- Listen for reload action
local CAS = game:GetService("ContextActionService")
CAS:BindAction("ReloadGun", reloadGun, true, Enum.KeyCode.R, Enum.KeyCode.ButtonX)

local firing = false
tool.Equipped:connect(function(mouse)
    print("Equipped")
    local user = tool.Parent
    if not script.Parent:FindFirstChild("ammo") then
        print("There ain't no ammo vals! better make 'ne")
        local a = Instance.new("NumberValue", script.Parent)
        a.Name = "ammo"
        a.Value = ammo
        local b = Instance.new("NumberValue", script.Parent)
        b.Name = "storedammo"
        b.Value = ammostore
    end
    mouse.Button1Up:connect(function()
        print("Button is up")
        firing = false
    end)
    mouse.Button1Down:connect(function()
        if firing then
            return -- The mouse is already down, and a loop is still running
        end
        local me = {}
        firing = me
        while firing == me and not reloading and ammo > 0 do
            -- Stop if reloading or someone else is firing, or I run out of ammo
            ammo = ammo - 1
            print(ammo .. " shots left")

            local ray = Ray.new(tool.Handle.CFrame.p, (mouse.Hit.p -  tool.Handle.CFrame.p).unit*300)
            local hit, position = game.Workspace:FindPartOnRay(ray, user)
            print(position)

            print(hit) -- This is used for debugging
            local hitted = hit and hit.Parent and hit.Parent:FindFirstChild("Humanoid")
            if hitted then
                hitted:TakeDamage(DAMAGE)
            end
            wait(FIRING_RATE)
        end
    end)
end)

you're problem begins on line 69 [;)]

You made a while loop loop without adding a wait, Roblox studio is so focused on running the script, It has no time to load your character, or anything for that matter.

Try adding a wait:

        while auto == true do
    wait(1/30)
        print("I can fire now")