How do I change CameraType on TouchEnded?

Errors in your code:

I. You tried to use the Touched/TouchEnded events on the client, use a RemoteEvent and fire the Camera change to the client, while handling the touch event from the server.

II. You are using deprecated code.RBXScriptSignal:connect() is deprecated, switch to RBXScriptSignal:Connect()

III. In line 4, CameraType holds an Enum value, although technically it’s okay to assign an Enum value with a string, if you are checking if an Enum property value equals a specific enum, you must specify the Enum in conditional statements. These are conditional statements, and if a property holds an Enum value, the Enum value must be specified. Take these for example:

if Character.Humanoid.RigType == Enum.HumanoidRigType.R6 then
    --code
end

while PlayerGui.ScreenGui.Frame.Style == Enum.FrameStyle.ChatGreen do
    -- code
end

repeat
    -- code
until game.Workspace.Part.Shape == Enum.PartType.Ball

IV. The event is BasePart.TouchEnded, not TouchedEnded.

--Server

script.Parent.TouchEnded:Connect(function(part)
    local plr = game:GetService("Players"):GetPlayerFromCharacter(part.Parent)

    if plr then
        game.Workspace.ChangeCamType:FireClient(plr)
    end
end)

Code for the remote event.

--Local Script

game.Workspace.ChangeCamType.OnClientEvent:Connect(function()
    local camera = game.Workspace.CurrentCamera

    if camera.CameraType == Enum.CameraType.Scriptable then -- Here was your error. Must check with an enum in conditional statements.

        camera.CameraType = Enum.CameraType.Custom --It’s always good to use enums instead of strings to assign enum values, since they are enums. 
    end
end)