I'm trans and here are my two cents on some of your questions

There is some concern that if gender identity is defined purely on self-identification, without any visible transition, cishet men will say they are trans to gain access to women's spaces such as women's shelters. And men go to a lot of lengths to endanger women, they do it all the time. So why can't we even talk about this? Trans women and cis women are both put in danger by cis men. Shouldn't we be on the same side trying to find a solution to this?

Why would a man claim he's a woman just to go to the women's bathroom? If a guy wants in the womens bathroom so bad he'd do it without an excuse. As for the deal with women's shelters, they could require the person to already be on hormones / some sort of therapy to allow them in.

Why is it transphobic to say that trans women have experienced male privilege? I looked up all these issues in the first place bc I saw the issue of Transparent where they go to the womyn-born-womyn music festival. At first I was like "wow these people are assholes" but then I saw how Maura couldn't accept that she'd ever had male privilege, even though she lived as Mort for decades and certainly benefited from some societal privilege there. It seems important to me that everyone check their privilege. As a lesbian woman I still have privilege that I have to confront. Why is it considered transphobic to discuss it?

You see, the concept of privilege is pretty bullshit nowadays because a lot of people use it to generalize the experiences of an individual, when it was originally built to generalize a population's interaction with another population (with EVIDENCE, not anecdotes). I find it being used to justify blind bigotry against people with 'more privilege' than trying to find solutions to problems that exist between populations.

I just really dislike the new concept in general, it oversimplifies complex issues by painting it black or white, which was not what the term was invented for in the first place.