You obviously have to use your best judgement.
And I mean they don't like your new partner after enough time has been given. Meeting someone once isn't going to cut it, but it also shouldn't take multiple years.
It can be nuanced, but for me, it's just not worth being with someone my kids don't like. At this point in my life I would probably introduce my kids by like maybe date number 4 and if they don't like him right off the bat I'd be leery. But they're adults. I certainly wouldn't do that with young kids.
It's part of the reason I had so much trouble with my last relationship. I waited way too long to introduce them, and I was already head over heels by that time. So I kept hoping it would change and it only got worse.