"I would never date a ______ person." I am sure you have heard some form of this before. Usually the blank is filled with transgender, but another common one is race. People seem to have strong opinions on either side that this is or is not racist or transphobic (etc). I think it is a form of discrimination and I will argue from that point of view.
The first question should be why the person thinks they would never date someone from a specific demographic. I know the most about the transgender argument and some of the points translate to other versions of the statement. Common responses are: "trans people are ugly/stand out", "trans people are infertile", "trans people have mental issues", and "I don't like penis".
The first argument that trans people are ugly or stand out and always noticeable. Usually these people totally disregard trans men. The statement is just confirmation bias. How do they know that all trans people stand out? There is no way they have seen and know who every trans person is. Any of the trans people they interacted with who didn't stand out aren't noticed. In general I think the people who make this statement are trying to conjure an image that all trans people look a specific way to make them stand out based on cherry-picked, incomplete observations.
As I said before the statement is usually made about trans women. Trans men having children is a huge topic that I wouldn't be able to speak on. As far as trans women the argument is usually something along the lines of: "Trans women can't bear children and I want children." I don't believe there is a huge issue with that statement on the face of it. The problem is with an inconsistency in logic and as a whole what I think is a sexist view of women in general.
Would they break up with someone if that person becomes infertile (accident, surgery, menopause, etc)? What if their partner is fertile but uses birth control to prevent pregnancy? Is this something that people speak about on a first date? If they are totally consistent they will answer yes to these questions. Women are just for procreation apparently. What about when the person they won't date already has kids? What about adoption? What about surrogates? There are alternatives and this is not a unique problem for trans people. If someone said this to me I assume that if they don't have as many kids (at least) as previous partners they are not applying this filter on anyone except trans people.
If the person doesn't outright say that being trans is a mental issue (it isn't) then they will cite secondary health issues. For some, maybe even many, trans individuals the secondary health issues, depression being the biggest I think, the cause is not being transgender, at least not directly. A person being trans is used as an excuse to ostracize, emotionally abuse, or physically abuse. Being unable to transition (if that is desired) is also a factor. The environmental factors around being trans causes these issues, not being trans. For these people a change in environment would help. For some having access to therapists and medications would help. It's unfair to place the burden on someone for something they are not in control of.
This argument falls apart as well because many people who are not trans have mental health issues. Those people don't appear to be undateable so why are trans people singled out?
As I have stated the argument is almost always used for trans women. This is made even more evident when the argument is that trans people have penises. It's easily falsifiable though because not all trans people have penises. Some have GRS. Some may be intersex. Some are trans men who could not or have not yet had surgery. It's an illogical statement from that perspective. Assuming the person mean trans women only though. The common retort to neovaginas is that it was a penis or that it's not really a vagina. I don't think there is any way to frame this other than transphobia. The issue is that they don't believe that trans women are women. How could they when they are looking at a vagina and thinking about a penis?
Outside of all of that is the issue that you don't know what the person has for genitals. Even if they don't have what you expect you would have to find out in a way that implies more than a casual date. If sex was on the table partners should be communicating.
I think, aside from the invalidation of trans people altogether, the issue is that people are too hung up on genitals of pre-op and non-op trans women. Men especially, think that if they like a woman and she has a penis they must be gay, meaning they don't think she is a woman. Lesbians assume that trans women will want to use their penis, if they have one, for penetration. For men I understand the societal pressures of masculinity, which I in this case are toxic. I know less about the woman side but I think it is likely there are pressures from some lesbian communities to be 'pure', which is similar. There are many who don't mind any configuration of genitals because they like the person not what is in their pants.
A likely diversion will be about homosexuality. A man arguing that the prejudices they hold are totally fine because otherwise they would have to consider dating other men, even though they aren't gay themselves! Again this assumes that trans women are not women as far as I interpret it. Why else would it be brought up if that wasn't the case? Let's pretend it wasn't invalidating though. A man not dating a man because he isn't gay is not the same as a man not dating a woman because she has a penis. It is ok to not date (blanket statement) a man if you are not a gay man because all gay men are the same in that specific way (they have a homosexual orientation). This does not mean that all gay men are the same in other ways, just the one specific way. There is no similar comparison for trans people, unless you add a number of qualifiers and that to me is not the same blanket statement.
There are many reasons that people will not date another person that are impartial. An extreme example might be dating someone with a disability that is incompatible with my lifestyle. If I am an avid mountain climber it is unlikely I will date a quadriplegic because they are unlikely to match with my lifestyle. This holds up logically for me. I still understand it to be a choice to exclude a group but without prejudice. It is ok (my opinion) to not like a penis/vagina genitals but distinguishing between impartial and discriminatory reasons matter when you voice your opinion.
With all these arguments you may notice that the common factor is that they are not intrinsic to trans people. All the arguments are based on assumption after assumption until they have only a caricature of what a trans person is. Why are extra burdens placed on trans people to be date-able that are not placed on everyone else?
Even after all this the people who make the statement will say: "You can't make me date ______ people!". The arguments are not about forcing someone to date or find a group attractive. They are to challenge incorrect assumptions. When I hear this I know the person has not absorbed anything and isn't willing (or capable) of critically thinking about the topic. All this is displaying is that they hold prejudices and discriminate. It's not about making or forcing anything. It's about trying to reduce the amount of discrimination and prejudice as much as possible. Thinking about things instead of blindly using blanket statements. If their statement was rephrased as: "I won't date anybody who was not born in _____ county of Texas" would they understand how they sound?
It is totally acceptable to apply individual criteria to each individual. There is a chasm of difference between saying that you would never date a specific trans person and saying you would never date any trans person. Using a simple race example: "I would never date Halle Berry." is different from saying "I would never date an African-American." Halle Berry has specific attributes that I don't find attractive, but African-Americans as a whole don't intrinsically possess those attributes.
Unfortunately I don't know if we as a whole will ever get over our prejudices but as individuals we can improve ourselves. I don't care if you limit your dating pool but at least be honest with your reasons or don't even tell anybody and keep it to yourself.