There isn't really any research either way that I'm aware of. Without knowing the likely cause of gender dysphoria, we can't really know if the factors I listed would be relevant.
That said, I think it's worth investigating. Here's a paper from Scott Kerlin, showing the results of survey from DES sons. It's a group of people born as male to women given DES, an estrogen affecting drug.
http://worldaa1.miniserver.com/~gires/assets/Research-Assets...
"More than 150 network members with “confirmed” or “strongly suspected” prenatal DES exposure status indicated they are either transsexual (pre- or post-operative, 90 members), transgender (48 members), “gender dysphoric” (17 members), or intersex (3 members)."
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A strong caveat to this would be that people don't just join a group called DES sons on a whim. A large number of women were given DES. Many more than 500 sons were born to them. People who joined the group are self selecting as having had some sort of problem or concern to discuss.
And that's almost all I could find on the topic. The only other thing that seemed notable is that the brains of transgender people resemble those of their chosen sex, not their birth sex. I.e. a MTF person had a brain typical of a women, not a man. But, this difference may only appear in adulthood, so it isn't clear if it is physiological or social.
If someone wanted to investigate this, investigating the testicular and endocrinal health of MTF people before transition would be a good start. If endocrine disruption had anything to do with it you would expect to see much more testicular cancer. The DES group had 5 out of 500 with this cancer, incidentally, while having a low cancer incidence overall.
I would categorize the published research on this topic as extremely slim. It's not even at the hypothesis stage, and your question isn't answerable without much further research.
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Oh also, while traditionally there were more MTF, recently gender dysphoria clinics are reporting more FTM.
Here are some numbers from the UK: http://gids.nhs.uk/number-referrals
The year on year referral increase is very large. So social acceptance/awareness must have a sizeable role. Endocrine dysruption can't explain a ~4x increase in 5 years.
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Edit: I should have included this: https://en.m.wikipedia.org/wiki/Causes_of_transsexuality
Doesn't touch on endocrine disruption in terms of estrogen exposure though.