Cloning a hat to the character with Filtering Enabled?

You could try passing the Hat value through the invocation as an argument.

Client:

local hat = player.PlayerGui:WaitForChild("ScreenGui"):WaitForChild("Hat")
hat.Value = script.Parent.Parent.Name
game.Workspace.FE.Hat:InvokeServer(hat.Value)

Server:

function FE.Hat.OnServerInvoke(player, hat)
	local Hat = game.ServerStorage:FindFirstChild(hat)
	if Hat then
		Hat:Clone().Parent = player.Character
	end
end

I don't know which line is line 26 so I don't know if that was the problem. If not, please elaborate. Hope this helped.

Explanation Edit: On the client, hat.Value is passed to the invocation as whatever the value type is (in this case, a string). The server doesn't even know there's a ValueObject involved-- all it receives is the value.

Let's say hat.Value == "Roblohunk". On line 3 of the LocalScript, before even invoking the server, the script gets the value of hat.Value-- "Roblohunk"-- and then passes it to the server. So, if hat.Value == "Roblohunk", line 3 is basically:

game.Workspace.FE.Hat:InvokeServer("Roblohunk")

This then passes to the OnServerInvoke function which, as you know, automatically takes the player who invoked as a parameter. That means the argument we passed is the second one, which I specified as 'hat'.

Considering the previous example where hat.Value == "Roblohunk", here's an explanation of the function:

function FE.Hat.OnServerInvoke(player, hat)
	local Hat = game.ServerStorage:FindFirstChild(hat) -- Find the first child named "Roblohunk" (or whatever hat.Value is) in ServerStorage. If a match isn't found, :FindFirstChild() returns nil. So the 'Hat' variable either becomes the hat, or nil.
	if Hat then -- We check to see if the hat exists (if it found "Roblohunk" in ServerStorage).
		Hat:Clone().Parent = player.Character -- If it does, we clone it and set its parent to player.Character.
	end
end

Hope this helped to clear it up a bit.