Unfortunately the answer isn't really that straight forward. There are many who mix different types of bta's without issue, but there are also many others who mix them and end up losing some. No one really knows what causes it, but generally speaking you don't want to mix wild caught and aquacultured, and there are some potential issues mixing certain other strains.
I personally have rainbows and greens together without issue. If you are going to try it, I would recommend starting them out on different sides of the tank if possible and have carbon on hand to run if anything starts reacting negatively.