You really don't understand us when we say that gender (aka the sex stereotypes and sex role stereotypes associated with the female sex) is a tool of our oppression, jj1968.
Or you wouldn't be presenting it as something we are privileged to be able to conform to. So I'll spell it out again: most if not all of the sex stereotypes and sex role stereotypes associated with the female sex come in a binary, that is a hierarchical pair, of which the stereotypes coded masculine and associated with the male sex are denoted as superior and those stereotypes coded feminine and associated with the female sex are denoted inferior. What this means for our lives is that we lose either way - we lose when we conform to those feminine stereotypes and we lose when we don't conform to them. We lose different things, it's true, but we lose nonetheless. What we gain if we conform is often of limited benefit and the punishment for not conforming can outweigh the benefits of doing so too.
Most of us here know this because we have tried both, which is why we have such a profoundly negative reaction to any attempts to enshrine the doctrine of gender identity in law. The international treaty devoted solely to women's sex-based rights, the Convention on the Elimination of All Forms of Discrimination Against Women or CEDAW, recognises the damage that sex stereotypes and sex role stereotypes do to the female sex and therefore calls on all member states to work to eradicate them. That would not be the case if stereotypes were beneficial to us.
And the stereotypes based on our sex are not the only issue we face, of course. Violent males attack gender-conforming women as much as gender-non-conforming ones, because of our sex. (And while the rates of male-on-male violence have reduced in recent years, the rates of male-on-female violence continue to rise.) Add to that the reality of our female biology, and all of the challenges it brings and we are dealing with a whole range of issues - many of which are again made harder to deal with because of the stereotypes associated with them. But all arise from our sex.
So no, females do not oppress males who identify as trans on the basis of easier gender conforming.
And it would make this discussion so much clearer if we could have a commonly agreed definition of what members of that group of males have in common beyond identifying as trans. The blokey bloke delivering a verbal declaration of identity is different from a crossdresser is different from a socially transitioned man claiming womanhood on the basis of adopting the stereotypes associated with the female sex is different from a post-op transsexual. All of these males identify as trans. Most of them are very obviously male to even a casual observer and none will be discriminated against on the basis of their gender identity because that is their innermost feeling invisible to the outside.
So is it transsexuals you are thinking of when you claim that women participate in their oppression? But if - as you are wont to claim - we cannot tell them from women, how can we do that? Is it crossdressers you're thinking of? Which of these males fall within the group you are claiming is oppressed by women and which do not? I would in all honesty be grateful for a clarification.
And this is not at all like claiming that white women cannot have an advantage over people of colour because they are female btw. We do know how intersectionality works. We do understand axes of inequality and that we can be on them or not, depending on what power system we're analysing. An individual is positioned alongside an axis of inequality depending on their possession (or not) of the dominant characteristic within a given power system. And sex stereotypes and sex role stereotypes (aka gender) are not a power system in and of themselves, but an expression of the power system of sex.
Finally, I've yet to meet an actual "cis-gender" woman. And I've met thousands of women and girls. I've met a few who call themselves "cis" but none of them are. In order for a power system to exist, its proposed dominant class really ought to be more than a theoretical concept dreamt up by sexologists in the 90s who described gender-conformity as healthy and beneficial. (None of them considered the role that stereotypes play in oppressing women. Obviously.)