There's this rising narrative going around that if you ask specifically for a CIS partner, you're a transphobe. That could be true for some people but it's not fundamentally related to bigotry. Moreover, this narrative, the "if you only want a CIS mate then that is prejudice" is trampling on one of the most important rights a person can have: the right to choose who they want to get intimate with.
First of all, transmen are in fact men and transwomen are in fact women. Let's get that out of the way. This isn't a foot in the door for "trans this really isn't that" narratives. What this is about it is the freedom to choose who you want to be intimate with. That right is sancrosanct, it is absolutely inviolable.
And yes, there's plenty of issues that make transgender dating a special issue. If someone reveals their TG status they can be open to hate crimes and even deadly violence. However all marginalized groups are special in their own way. As a black man I don't think it's racist if a woman says she doesn't want to date a black man. I face oppression, too. My class is special in its own way. One group isn't more special than the other. None of us have the right to force ourselves upon those who don't want to be intimate with us, even by omitting who we really are.
Really, if you have to deceive or hide who you are in order to date someone, do you really want to date them? I wouldn't. That's not fair to you and you're denying them their right to choose who they want. What do you think will happen when the person wants a CIS mate and they discover the truth? They're going to get pissed and dump you. Now you have to shame them into staying with you: "If you loved me for real this wouldn't bother you"... that's not going to convince anyone. They're either going to leave, or they'll resent you forever. That's just how it is. You can be mad at that but that's about as effective as protesting the rising of the sun. There's just no way to win once you've gone down that road.
"I want a CIS mate" is not the same as "trans women are not women" - one is a preference, the other is harmful prejudice. On the flip side CIS people who do date trans people shouldn't be shamed for their choices either. A man should be free to date a trans woman and not catch flak about it. Trans people should be able to be openly trans and not face hate speech or threats to their well-being. This, without any exception whatsoever.
The fundamental fact is when you shame or worse abrogate people's right to choose who they want to get intimate with, it's not going to end well for you. All you're going to get is people who resent being coerced or bullied to date people they don't want to. And that's not something the country, or the world, will ever put up with. Except that right now, most people don't imagine they can be labeled a transphobe just for wanting a CIS mate. And unpopular opinion: that should be nipped in the bud.
A transwoman has a vagina post-op. But again this part is irrelevant IMHO. Freedom to choose is sancrosanct. If you date a transwoman it should also be with zero consequence.
You're correct, dating the type of person you actually want to date should come with no consequences or judgement.
Some people might prefer an uncircumcised penis or natural breasts, some people might be indifferent, and some people might prefer breast implants or a circumcised penis. It's no one's business what someone prefers and no one should feel bad for having a preference.
It's kind of a crazy thought that you would judge someone who is turned off by breast implants for not dating a woman with breast implants. I feel the same logic can be (and for the most part is) applied to preferences or indifference for post-op genitals.
There are definitely a vocal minority who would say that having a preference for cis partners is transphobic, but I doubt most people, even most trans people, would consider you bigoted for having that preference.
EDIT: I doubt you're encountering enough trans matches to need to put your preference in your profile.
Forgive me, but I'd say a vagina, or lack thereof, is pretty damned important to most of us.
If a woman started out with a penis? Meh, I might go for that. But I certainly want to engage in "normal" sex, and there's nothing wrong with that. And I'd think you agree.