I feel that lore-wise, the doctor changing sex was a bigger test of suspension of disbelief. But they prepped for it by having the Master do it. The Master has previously spent time being a walking corpse, so that is a fairly straight line of baby steps to get there.

Once that's been established, changing race is nothing. And arguably the doctor has shown a not insignificant amount of racial diversity already to prove it's not impossible.

The show just sucks for a variety of other reasons.