Course, they'll tell you to talk it over with your surgeon.
In my experience, surgeons know about their procedure. They don't really know about rehab and follow-up because they don't do much. They see you to prepare for surgery. They see you at surgery. Then, you have maybe two or three appointments as you are healing and then......bye bye!
So what would they know about it?
(In fairness, they may hear about it when someone has a replacement and then runs into trouble from...whatever.....an infection, too much use, etc.)
They used to tell people with a replacement that they could not do anything really physically stressful. But, that has changed. I know guys who play tennis and jog and.......
I don't know if there is any information on Crossfit. I know with the jogging people can run into problems with fractures, dislocations, loosening of the prosthesis, and even the scraping off of small metal fragments. But they say those things are really rare.
Now, it seems to me that jogging and tennis would be harder on a joint than Crossfit because those activities produce more pounding. But, there is the weight used in Crossfit to be considered, and I picture the angles of the hip in the deadlift and the squat.....I don't know.
Here's a link to a big study on running and other sports:
https://www.ncbi.nlm.nih.gov/pubmed/25383251

I do know people who play tennis afterwards, and their surgeons are okay with it.
Good luck!