I've been with someone for about a year and a half and, mainly because it's long distance, I'd never thought much about the fact that he ate animals. He's always been very respectful of my choice to be vegan, which I have been since long before meeting him, and so it never really came up in a context other than discussing veganism (no mention of how great his animal-based meals taste etc). Then, about a year into our relationship, he decided to become vegan or almost vegan - I can't/wouldn't exactly inspect everything he buys but he goes out of his way to get vegan foods even for catered work parties and such.
After my partner became vegan I got to thinking that if he hadn't, it definitely would have been a problem for me after a while. I couldn't be with someone who, after being informed about everything wrong with the meat and dairy industries, as well as other forms of exploitation, wouldn't make a change. Eating meat or dairy is not a personal choice. It's a decision to deliberately and directly cause the suffering and deaths of animals. As a vegan even "humane" farming is wrong to me - animals are not ours to use and I simply don't have enough in common with anyone who believes they are to form a meaningful relationship and I feel more strongly about that the longer I am vegan. As I said, it was easy to overlook when I never had to be around the smell of an animal being cooked or my partner's flesh breath or anything, but if he hadn't gone vegan I think it would have been only a matter of time before that started getting to me.
As for whether it's objectively hypocritical, I'd be a hypocrite myself to say it is. Some people say you're supporting their lifestyle by being with them and I don't necessarily agree - my brother in law for example eats vegan at home and for his packed work lunches but occasionally eats an animal when he's not around my sister (who's also vegan). So everything my sister is a part of in their relationship is vegan, and everything non-vegan her fiancé does is his own thing. The only thing that stands out as a problem for me is the moral implication of accepting the fact that someone kills animals on a regular basis even though you're against it, but we need to function in the world and in order to do that we overlook that moral difference every day in almost everyone we meet anyway. I got with my partner because there is no one else like him, he's incredibly sweet and kind and we understand each other in a way that is extremely rare for both of us, so even though we had a fundamental disagreement about animal rights I feel he is valuable (for want of a better word! special?) enough for me to get past that. And that turned out to be a good judgement in more ways than one when he decided to stop consuming animal products.
So really I think it all depends on the individual. Do they eat animals without really thinking about it, or are they the type to mock vegetarians or turn up their nose at a plate of vegetables? Do they seem open to new information and the possibility of changing their lifestyle to be less harmful, or do they figuratively block their ears whenever you bring up the topic of animal rights (or other important subjects)? Are they a generally kind person who seems unknowingly ignorant about their diet, or do they just not care? These are questions I believe veg'ns should be asking themselves about their partners or prospective partners before getting too invested, if possible. If the person fits into the former categories then I see nothing wrong with getting into a relationship, being patient while you share your views/information, and giving them a chance to change because you have no reason to believe they'd make the wrong choices if they were aware. Either way, so long as the financial aspect of supporting animal exploitation is at least kept separate then I'd say it's a personal choice whether to date someone who disagrees with your morals.