stede doesn't judge ed for having sex with jack, but importantly this is not because he is magnanimously choosing to overlook something that reflects badly on ed. it's because it would straight up never even occur to stede to judge anyone (and especially not ed) about their past sexual choices. (one of stede's funnier character traits is there's things he can be judgy about but others where he is almost autistically oblivious to a thing that a lot of people judge others for, and this is one of them.) if you have trouble liking or respecting ed teach despite knowing about his hilariously awful taste in exes stede bonnet would tell you that's a skill issue.
jack on the other hand also does not judge ed for his other sexual partners - as he says he thinks there would be no shame in it if stede and ed were already buggering each other even if he's had his own dalliances with ed before, he'd agree with pete's "we don't own each other" as far as that goes - but for completely different reasons. jack isn't bothered by ed having sex with other people, including people jack doesn't like or respect, for exactly the same reason he's so sure it WILL bother stede: because jack sincerely thinks of monogamy as a pathetic hangup for losers and landlubbers. he doesn't have a particularly enlightened view of sexual ethics, he hasn't invented ethical polyamory in any kind of modern sense, he just thinks trying to exert control over who else your fuckbuddy might sleep with would mean admitting that you care about the relationship on some level, and as far as jack's concerned caring about things is gay (derogatory). real pirates have dalliances, not relationships.
what jack's doing here, by bringing it up, is the same thing he's doing throughout the rest of the episode: providing stede information that he expects stede to find upsetting and challenging stede to react to it the way a Real Pirate would. a real pirate would have fun with turtle vs crab. a real pirate would love coconut war and if you got bonked in the head you'd bonk someone right back. a real pirate would think it's awesome that ed set a shipful of guys on fire one time, like jack does. a real pirate wouldn't care who else his crush wants to fuck, like jack doesn't care about it.
“Ed’s past is Ed’s business, and I respect that.”
Then Jack escalates it because Stede calls him Ed.
All this, and Jack also, if looking at him from a narcissistic perspective, doesn’t like that Stede doesn’t take the bait. Stede continues to be calm, continues to respect Ed, and Narcissists don’t like not being the center of attention or not being right. This is why it feel like to me, when Stede doesn’t concede, Jack has to got to a physical altercation (pissing on Stede’s boots) because he realizes his normal verbal tactics won’t work.
To all this it's just Jack's explicit goal the entire time to drive a wedge between them. He fails at getting the rise out of Stede he wanted about comparing what could be between Stede and Ed to "dalliances" --the real rub there is to make Stede feel like he doesn't matter much to Ed-- but he correctly predicts he'll get a rise out of Stede about the violence and disrespect, thus prompting Stede to tell him to fuck off, allowing Jack to pull Ed away with the life debt guilt.
Whether anything Jack says or does to this end is true or sincere doesn't matter. We can assume the life debt is true. He still only brings it up to get Ed to do things. He can tell the truth as manipulatively as he can lie. All that matters is he's a wedge in the shape of Ed's old life that Ed overcomes.
I get the sense that Jack thinks Stede will be sensitive or prudish about sex and then Stede responds in a way he doesn’t predict. So he keeps escalating it.
I genuinely don't think the sex comment stopped at the assumption of prudishness though. He uses a word to deliberately downplay Stede and Ed's relationship as not meaning anything because he's correctly clocked that Stede has an emotional investment in Ed. Calling it "dalliances" after calling it buggering (which was used to be crass) is about the insult of being frivolous. That Stede isn't special to Ed, and while Stede responds maturely in the moment, I don't think that escaped him especially after Ed's (claimed) willingness to leave the previous episode.
Stede knows how to take passive aggressive comments like that and play it off, but you can tell he's not just upset about being peed on. It's the insults to how close he and Ed can even be. And yes, Jack keeps escalating it right to killing Karl because that's just his specifically stated mission here.