How to fix "attempt index nil with 'LoadCharacter' " ?

You are attempting to get the player from your function .MouseButton1Click(), however .MouseButton1Click does not create an output. Alternatively, you can use game.Players.LocalPlayer as you are using a LocalScript. Here is the API Reference for MouseButton1Click: https://developer.roblox.com/en-us/api-reference/event/GuiButton/MouseButton1Click

local plr = game.Players.LocalPlayer
script.Parent.MouseButton1Click:Connect(function()
    if  game.Players.LocalPlayer.TeamColor ~= BrickColor.new("Medium stone grey") then -- check if player choosed team (if (s)he not choosing team)
        game.Lighting.Blur.Size = 0 -- Makes blut size to 0
        plr:LoadCharacter(plr) --Refresh character
        script.Parent.Parent.Parent.Enabled = false -- Makes GUI not enabled
        script.Parent.Parent.Parent.MenuMusic:Stop() -- Stops music
game.Workspace.Camera.CameraType = Enum.CameraType.Custom -- Makes default (custom) camera

        print(game.StarterGui.ChooseTeamGui.ChooseTeam.Frame.Visible )
        --If player dont choosed team (if (s)he choosign team --
    else
        script.Parent.Parent.ChooseTeamWarning.TextTransparency = 0-- Makes warning text visible
        wait(1)
        script.Parent.Parent.ChooseTeamWarning.TextTransparency = 1-- Makes warning text invisible
    end
end)

Hope this helps!