Over the past two decades, as hip replacement surgery has become more common, doctors have become more liberal in allowing patients to perform more activities. Patients undergoing hip replacement are now younger and remaining active for longer. Many patients who have hip replacement continue to participate in sports and activities that require running or jumping--so-called high-impact activities.
Recent research has shown what many doctors fear--that these impact activities will cause accelerated wearing out of hip replacement parts. The data seem to show that hip replacement wear is often related to activity level. This is a concern, as performing surgery to replace a worn-out hip replacement, a revision hip replacement, is usually a very complex and difficult surgical procedure.
It's hard for patients, because even surgeons who specialize in joint replacement surgery disagree on recommendations for activities after surgery. However, this study would indicate that any impact activities, activities that require any running or jumping, should be avoided.
Sources: "Does Impact Sport Activity Influence Total Hip Arthroplasty Durability?"

Thanks for the article Jonathan, I’m going for a hip replacement and have been told different things by different doctors so this was really useful
I agree that there’s a lot of discrepancy with regards to what you can do after surgery. My doctor has told me that there will be certain activities I should avoid after my hip replacement, however, my uncle found that after a few months, he was able to perform all of his usual activities.