I have an RBTA (recently split into two) and a single GBTA in my 29 gallon. They are relatively small though. Maybe 4", 3" and 2" respectively.
So, I'd say yes you could keep an RBTA just fine with that size tank. The lighting is probably ok too. I have a 175 halide myself. As others said it will sting your corals. I have to keep an eye on things and shift my other corals around. At the moment a Xenia is getting harassed (I don't care), and a small green slimer (I do care). I typically feed them mysis maybe once a week at most. If I feed them more frequently they tend to grow a VERY fast. Once a week they grow slowly. The BTA's will be just fine and they will get some additional food from the water column as you feed your fish. The key is clean water (skimmer) and stable parameters. Keep those nitrates low. BTA's seem to be less demanding and hardy. I have never had problems with them. My tank has been running for 9 months now.
My skunk cleaner shrimp is fine with the BTA's. It actually knows how to handle the anemones and even occasionally steals food from them. It delicately pokes the tentacles until they retract and moves in for the grab. It doesn't seem to bother the BTA's all that much. But, if the shrimp takes a wrong step I suspect it could easily become a meal.
As with any anemone, careful if you have any power-heads. They can wander around a good bit until they find a spot they like. Stinging whatever crosses their path, and potentially becoming puree in a power-head. Once they settle down, the risk drops greatly, but the risk is always there. I have two Koralia power-heads in my tank and it hasn't been a serious problem. However, when my RBTA split, one of them decided to wander all around the tank and eventually parked itself right on a power-head. I noticed it heading that way and unplugged it, though it managed to get some tentacles chopped off. Eventually it became confused and stuck in that corner of the tank. I removed it by hand and placed it in a part of the tank I thought it would like. I was right. It loves it's new spot and has been there for weeks.
I'd suggest getting an RBTA from a BRS member rather than the LFS. Unless the LFS BTA is colorful and looks healthy. Mine have been super healthy and you get one knowing that it is a split rather than wild harvest. Also gives the potential that it will split for you eventually too!