Why won't the following code work? Issue with GetPlayerFromCharacter

You should always check to see if player exists because sometimes another part may touch the part the event's connected to, and GetPlayerFromCharacter will return nil.

Also, you should note that using Instance.new's 2nd parameter is not advised, because of performance issues

function onTouched(part)
    local character = part.Parent
    local players = game:GetService("Players")
    local player = players:GetPlayerFromCharacter(part.Parent)
    local shirt = character:FindFirstChildOfClass("Shirt")
    local pants = character:FindFirstChildOfClass("Pants")
    if player then
        if not shirt then 
                shirt = Instance.new("Shirt")
                shirt.Parent = character
        end 
        if not pants then 
                pants = Instance.new("Pants")
                pants.Parent = character
        end
        if player.Team == "Red" then
            shirt.ShirtTemplate = "rbxassetid://136056214"
            pants.PantsTemplate = "rbxassetid://136056214"
        end
        if player.Team == "Blue" then
            shirt.ShirtTemplate = "rbxassetid://136056667"
            pants.PantsTemplate = "rbxassetid://136056667"
        end
    end
end

script.Parent.Touched:Connect(onTouched)