There are no fish safe anemones. I even know of an aptaisa that ate a tiny goby. "Carpet" anemones typically don't move much once they're happy, but if you're looking for an anemone that won't eat your fish, I wouldn't advise "carpets". They are very well equipped to capture and eat fish.
What happened with your BTA and tang is very rare. If your fish are healthy and you give them plenty of swimming and hiding space, you may never lose another fish to your BTA.