Also, frankly, I think that on some level I'm not really sure it's even that much of a problem if Rhaenyra has a reputation for occasionally flying off with cute noble boys as long as she doesn't get pregnant and isn't clearly attached to some boytoy without being properly married to him.
Alicent would have had problems, but that's because she'd be riding off with a guy nobody knows and who may not even be a noble- someone who has no reputation and isn't accountable for his actions.
With Gwayne or Steffon? I think maybe it's the "there will be rumors" level, not the "these rumors actually become a problem" level.
I think the gender thing makes it so that
any rumors that we're having sex are a problem. Remember Saera Targaryen, and canon!Alicent's reaction to her believing Rhaenyra had slept with Daemon - and then learning she did sleep with Criston. The rumor that we're "loose" is about as bad as the rumor that we're having an affair, and it casts doubt on the legitimacy of any children we do have.
Maybe rumors about a female "favorite" could be okay - as it can never result in illegitimate children and a lot of the attitude would be that whatever two women do is never "really" sex. But IMO we should never have a male partner we're not married to or allow rumors to spread to that effect.
I think the perception that we're engaging in romantic courtship without sex as a prelude to marriage, but which doesn't have to result in marriage, would be fine and probably even beneficial.
I dunno, talking to him might grant an interesting perspective on politics from another angle, or he might turn out to have some potential we could benefit from cultivating?
I mean sure,
maybe? But this is also true of guardsman #15 or #20, with the only difference that we don't actually have an option to talk to those people.
If anything I'd think that a literal arbitrary random knight might be
more promising as either another perspective or someone to cultivate. Most of the things we know about Steffon actually give us
less reason to actually talk to him. Jeyne picked him. Assuming Jeyne is at least reasonably competent, she'll have vetted him, and she'll have selected someone for both their capability and their loyalty to her. So we shouldn't need to seriously vet the guy. We likely don't need to win his loyalty as long as we have Jeyne's friendship, but if we wanted him to be more loyal to us than Jeyne it would probably be a
very involved processes (and have no real benefit unless those loyalties ever conflict).
I'm in favor of taking a train action with the guy at some point before the end of the progress, or a conversation action if for some reason we can't, to both sell the fig leaf & to do some basic checking that these assumptions are true. But this is not a priority at all. He is someone to fit in the schedule where we can, not someone we take on dragonback. Maybe when we do talk to him we find out that he's more than that, but "maybe if we talk to him we'll find out there's a reason to talk to him" is not a good reason to prioritize it when there are other people we actually know of reasons to talk to!