Here’s another case: Canadian Prime Minister Pierre Trudeau was occasionally accused of being a Communist, for being friendly with Castro, sheltering Vietnam War deserters, and early leftish activities and associations (which did get him banned from entering the U.S. in the 1950s). He was not, as far as I or anybody else knows, actually a secret agent of Moscow, with a KGB controller, and other spy story accessories.
But to the Cuban, Red Chinese, Vietnamese and Russian Communist beneficiaries of his policies, did it matter?
Could Barack Obama announce he is a Muslim after he leaves office? Of course he could. It would be self-indulgent, it would damage both his party and his country…of course he could.