A lot of what you have heard or seen is more rooted in the extremism, not necessarily representatve of most transgender people.
The statement of some radfems that trans women wish to force lesbians into having sex with them or end brand them as a transphbobe is one of those really frustrating things that plagues the majority. I know there is indeed a minority who feels this way, in the same way that some gay people are Trump supporters- it's baffling, is in no way representative of the views of all trans women, and I have been vocal about that for a very long time.
In November of 2018, someone posted a photo of a woman on twitter and said "Is it gay to think this person is attractive?"
I responded; "I'm not attracted to her. She's beautiful, sure. I wish I looked like that! But not my type. Does that make me lesbo-phobic if she's a lesbian? Transphobic if she's trans? Racist if she's not white? Which phobic does my lack of arousal imply?"
Turns out the photo was of a trans woman.
In December of the same year, a woman was raging on twitter about transgender lesbians implying a sentiment similar to what you mentioned. Here is that exchange:
@Peachyoghurt_YT Dec 15, 2018
If we lesbians should work through our disgust and learn to love penisis, then why can't trans people learn to love their own genitals?
@phaylen Dec 15, 2018
I'm a trans person. I don't think you should "Learn to love penises"
Has a trans person told you that you should, or have you subscribed to the extremist nonsense spewed by conservatives that just claim we do... This is the "War on Christmas!" argument. It's not real.
@Peachyoghurt_YT Dec 15, 2018
This is something lesbians have to deal with, it's real. We get kicked out of LGBTBLAHBLAH groups for saying we don't do penisis.
We get called bigots, vagina fetishists and transphobes. I kid you not.
If someone forces you're into a sexual situation with someone you're not attracted too, that's rape. It is not transphobic to express sexual disinterest in anyone you don't find arouses you. It is transphobic to abuse someone simply because they are transgender.
That seems like common sense, right? No human is under any obligation to surrender their autonomy to anyone else. No person assigned female at birth has had a trans woman demand she give up agency of her sexuality.
That is not to say some trans women don't feel incensed by the preoccupation with our genitals. As women of the trans experience, it is important to note that does not have a relationship with our sexuality. Some trans women wh were born male still prefer the sexual company of women. Other trans women prefer the company of men. What you might find surprising is that the majority I've know prefer each other given the extremely narrow dating limitations. I'll refer you to those trials outlined here in this article on the topic. https://medium.com/@Phaylen/a-letter-to-the-lesbians-who-hate-me-32dcafc0893
I am asexual. I don't pursue sex with anyone. It isn't something I need to have in order to maintain a healthy social or mental state. Does that make *me* transphobic? Alternatively, if a lesbian takes an interest in me- and they have- and I rebuff those advances- am I lesbophobic. The people making such claims regarding transgender women can't have it both ways.
However, I also know trans women in beautiful and healthy relationships with women assigned female at birth. I also know transgender men in happy gay relationships with men assigned male at birth. I know transgender men and transgender women who are together having families. It boils down to individual compatibility.
But, the biggest indicator- and one often looked over- that demonstrates that this is an issue manufactured to harm explicitly transgender women- is the absolute lack of gay men attacking transgender men claiming they are trying to "Attack them with their vagina-ed bodies!" Or, are erasing their gayness by virtue of existing as gay men, or that trans men are forcing gay men to have sex with them in order to exert social dominance.
Maybe you might find one or two gay men who believe this or feel this way, but the majority would laugh at the sheer absurdity of it.
Indeed, most of the signaling from radical feminists are typically heinous, inaccurate narratives fed to them by our detractors who benefit from their fear and leverage them as attack dogs exclusively against transgender women.
Sports- and issues regarding that- is a complex issue. I agree that there should be stringent guidelines in order to qualify to compete, but it must be measured. Remember, there are actual women like Caster Semenya, who are being criticized for simply appearing to masculine and performing to well. https://www.nbcnews.com/think/opinion/caster-semenya-being-forced-alter-her-body-make-slower-runners-ncna1000896
finding a reasoned resolution that makes sense to all involved is possible if we could move beyond opinions formed by an embedded prejudice.