You're putting the code in the ON CLICK event. Put them on the AFTER UPDATE event. Because they're checkboxes, you don't have to be explicit, i.e. "If Me.EURO = True Then". You can just use a the shortcut, "If Me.EURO Then". You don't disable them, you're just checking/unchecking them.
Private Sub GBP_AfterUpdate()
Me.EURO = Not Me.GBP
Private Sub EURO_AfterUpdate()
Me.GBP = Not Me.EURO
Michigan Dept. of Environmental Quality, Air Quality Division