To what end goal? Given her positions, conflict seems inevitable down the road, and we don't actually gain anything from delaying it. Whereas now we can get a bit of a stress reduction, which is nice. Even in pure game terms it's something minor vs, well, probably nothing.
I mean, she's hoping for a daughter here, which is a good sign if she just never figures out. We do gain from delaying it as well. For starters, we're currently about to leave for 12 months, and she'll be free to politic unattended, which won't be the case later. Also, if the fight starts
after we've established a relationship with our siblings, then it'll be harder for her to deny access or sabotage those relationships.
Like, Johanna is clearly somewhat traditionalist (she's tied to religious homophobia and wants to pass on her mother's things to her daughter)
I think this is somewhat complicated. She seemed perfectly okay with us being a knight, and canon!Johanna led armies in mail. She also isn't assuming we're gay, despite us dancing with Jeyne and training. It's also interesting that she seemed to view lesbians as worse than gay men. While she mentions the gods she also doesn't seem to be quoting scripture (although maybe she is and we just don't know it well enough to recognize it). We also note that she's thought about this and put effort into justifying her beliefs to herself - this doesn't sound like a reflexive and unconsidered bias.
I'd kind of been hoping her views were her repressing, but that also seems unlikely since she wouldn't be asking questions about why wlw exist, it'd be about giving into temptation.
I think Rhaenyra picking her battles here isn't out of character - while she's dedicated and unafraid of making enemies when the outcome is important, the only outcome of this fight is a fight (+ stress reduction). She's also at least somewhat canny politically.
Also… if we wanted to fight her we just never should have talked to her in the first place. The point of this conversation was improving relations.
[X] Give your support to one the names she suggested
-[X] Aelora
[X] Ask how her cats are doing
Edit: Alternatively, what about this as a write in?
[X] Write-in: Tell her that jealous men have been spreading such tales about you ever since you took up the sword, and that you have learned to pay little heed to rumormongers. You danced with Jeyne because you did not wish to give anyone ideas about marriage.
The idea here would be to present rumors about homosexuality as the product of something she doesn't seem to mind.