Have you googled 'yoga after hip replacement'? There are lots of articles about it and maybe some will help you and your surgeon to get on the same page.
Although yoga isn't my thing, just yesterday I did a little googling because a few yoga-ish moves had been added to my pt routine. They were contraindicated because of the couple of restrictions my surgeon has in place for me, and I was looking for modifications. You can check it out yourself but my basic takeaways were it depends how far out from surgery you are, and which approach was used.
I don't practice yoga, but I have other other activities that are part of my lifestyle. At one of my early post op check ups, I asked about one -
Me- Can I do this?
OS - AAACKK! Dangerous! No!
Me - But I need to!
OS - Well, just be careful and do it this way, don't do it like this, etc
Me - Ok, thanks for the instruction.
At the 6 month office visit -
Me- Can I do this other thing?
OS- AACCKK! Dangerous! No!
Me - It's really important to me. I had this surgery so I could resume my former activities.
OS - Well, do you think you can find a way do do it this way instead of that way?
Me - Yep, I think so.
OS - Just remember that we don't consider replaced hips fully mature or healed for about a year. So I'd rather you hold off for a while, then try the way we've talked a out. Go slow and thoughtfully, no forceful quick movements, and if it feels weird or hurts, stop.
Me - Cross my heart. Thanks for understanding.
Maybe if you approach your yoga practice the same way with your OS, he'll give you a go ahead also, for at least some of your poses. It won't hurt to ask and he might surprise you. From what I read yesterday, I would bring along diagrams to show him what each looks like, and be ready with alternatives as well.
Good luck. Best wishes for happy healing.
Edited to add informative link https://yogainternational.com/article/view/how-to-approach-yoga-after-a-total-hip-replacement