I'm going to have to disagree with the other poster on this one. Rhodactis mushrooms can absolutely be invasive, it just depends on the type. If you're getting the really nice colorful ones, they tend to grow more slowly. However, I have a green hairy mushroom (also a rhodactis) that has grown like wildfire in my tank and has taken out everything in its path, including other mushrooms.
See the single hairy mushroom on the middle of the right rock below the Xenia? This was August 2019.
Now here's early December 2021. They out-competed the watermelon and blue discosoma mushrooms beneath them and have pretty much taken over the right rockwork.
Don't me wrong, I'm not trying to discourage you from getting these beautiful corals, but under the right conditions they can go nuts in your tank. I happen to like them since they look a lot like anemones when they get larger. I certainly could have pruned them back as well, but I've taken a bit of a hands off approach with this tank.