First off, marrying fictional characters is fine and good. It gives more meaning to the institution of marriage when people get innovative with it.
The issue here is that it's through a proprietary subscription-based service, Replika. The company could opaquely and fundamentally change how her boyfriend functions and is controversial for having done just that. I don't think that's a safe foundation for a strong emotional investment.
We do, for better or worse, get deeply emotionally invested in characters we don't control the canon of. But usually we have the option to simply ignore new canon and still interact with established canon. Not so here, where the service is live and ephemeral. A Replika AI can subtly monetize the relationship, cease offering certain comforts, or simply shut down one day if the company folds (or the human stops paying the subscription).
I suppose this is an issue I have with all multiplayer-centric gaming experiences: I prefer to invest myself in games which can be preserved indefinitely. Though obviously there is a unique value in multiplayer interactions, *because* they're always evolving and making the most of a finite life...
sidenote: Now I'm imagining AI WoW bots trained for specific builds of the game, to roughly simulate the experiences. Like a museum animatronic, obviously fake but close enough to convey the history or invoke nostalgia.
But yeah I think I'd only marry an AI if I was in a serious relationship with a person curating that AI. Or if I made it myself, and I don't mean "fed some inputs into a black box". The software would need to be open-source at LEAST, even if chose not to look, because then I can theoretically run it myself if necessary.
oh or an actual free sentient AI, obviously, but that's not real yet
quickedit: Sarah Z did a good video about Replika specifically. The controversy, the monetization, the uncanniness, and notably the emotional connection
https://www.youtube.com/watch?v=3WSKKolgL2U