I have never heard of antispecism and a quick google search leads me to believe that is a little, uhm, extreme.
I have a friend who’s a vegan and her partner is an enthusiastic carnivore, who also loves to hunt and fish.They seem to have made that work for going on 5 years now.That said, she’s not a “vegan missionary”, never criticizes others eating behavior and is also not overly paranoid – by that I mean that, for instance, she and I once stayed in a “vegan AirBnB” where it said in the description that “absolutely no meat was allowed in the apartment” (true story).This was a coincidence (only place available) and never ever would my friend say or expect anything like that.I lived with her on-off for a few months when travelling and was perfectly allowed to do whatever I wanted in her kitchen and that included using the knife to cut meat We go to vegan restaurants occasionally, as does she with her carnivore partner, and we all go to non-vegan restaurants too, where she simply orders stuff that is actually vegan while letting us go about eating whatever we want to eat.

Can’t remember her ever making a comment to anyone about it.
Personally I’m a part-time vegetarian, have no interest in veganism, and generally couldn’t care less what other people eat or don’t eat, as long as everyone just leaves each other alone.
Bottom line: if neither is an asshole about their eating habits or that of the other, I can’t see why this would ever be a problem, not in a friendship, not in a relationship.If it turns out to be a “you’re doing everything wrong and shame on you for XYZ”, then yeah no, that wouldn’t work.But that’s true for everything.
From what I read though, the eating habits may be the smallest difference and/or potential issue here.

And I second others’ comments, you already seem to be somewhat hesitant, so I’d say listen to that, give it a bit of time to develop, but apply a certain level of caution..