Not really. EE2 is used in birth control but the spike in people being transgender (or being openly transgender, at least) does not line up with the adoption of EE2 BC (which started in the 1960s - if that was the case you’d expect to see a bunch of transgender people who grew up around then, so ages 50-70). Further, spikes in EE2 cannot explain the prevalence of female-to-male transgender people.