There is no female privilege. People (both biological females and biological males) are socially rewarded based on their ability to perform or fit within a culture's idea of feminity, not what's actually between their legs.

Many women get misgendered based on shalow traits like hair, clothing, skin,etc. even though they're biologically female.

https://www.buzzfeednews.com/article/hannaheko/aint-i-a-woman

Some transwomen who are perceived as more feminine get privileges that ciswomen who are considered less feminine don't get. (Men thirsting over a transwoman at 3:06.)

https://www.youtube.com/watch?v=DazZ_NfPkN4