Nope; it’s not. Totally social. Ask any trans person; I know many and this has come up in the past.

It’s not social at all, transexuals can attempt to mimic this but your precession is dependent on your pelvic structure.

Any forensic or surveillance grade gait analysis software can easily distinguish between the sexes and it’s not fooled by sex reassignment operations or sexual orientation.

I am very skeptical of this claim. There is enough variation between individuals of either gender to make positive identification close to impossible (not to mention that muscular / ligament changes in the hips on hormones can cause the hips to rotate over time into a different position). Sexual dimorphism in humans has such significant overlap and grey area that positive identification from physical characteristics alone is going to have a significant error rate.

There is a good documentary on this. It focuses mostly on voice but the source is similar: https://en.m.wikipedia.org/wiki/Do_I_Sound_Gay%3F

They may appear that to you not to gait analysis software.