Maybe it is (I'm not so sure but I'm open to the argument), but even if true, it's a completely separate thing from someone buying a home and renting it out.

The homevoter hypothesis is mostly nonsense. There isn't a coordinated, conscious effort to restrict the supply of homes based on rational expectations of excess returns. People restrict the supply of homes due to misguided aesthetic reflexes, racism, nostalgia, and a bunch of other stuff, not because they are mustache-twirling capitalists.