There's always that ONE person who says, "yes, I've done it, I don't understand why you can't do it." Yet there are 100 other people who say don't do it because they've tried it and failed. Anecdotally speaking, that means it probably shouldn't be done because the rate of success is low.
And no, they don't talk to each other (obviously). It just so happens that the more expensive anemones (CSBs, ChSBs, infernos, etc.) are the ones that are less widely available in the hobby, yet the demand for them is relatively high--supply and demand dictates the higher price. Rainbow, red and green BTAs are common and reproduce quickly so the price is low. Shermans, Black Widows, and purple passion morphs tend to be in the middle of the pack. Wild BTAs tend of be all over the place in terms of price and the rate of success equally varies.
And yes, they're all BTAs so they're the same species, but some people assume they're just color morphs so therefore they're all the same. But that's not necessarily correct. I believe that color indirectly indirectly affects the BTA's hardiness--it could be due to different species of zooxanthellae within the BTA and that zooxanthellae could affect a BTA's color. For comparison, different color morphs of SPS behave similarly, such as Acropora youngei--the green slimer is a quick grower and is extremely hardy while the blue yongei doesn't grow nearly as fast and tends to RTN/STN at a higher rate than the green morph. Same species, just a different color.
If you were to try it, here's what you should do to maximize your rate of success: run lots of carbon as well as an oversized UV sterilizer. This is done to mitigate chemical warfare, aka allelopathy. Some people also believe the low rate of success mixing BTAs could be due to bacterial infections, but if a BTA is properly treated for bacterial infections (typically with Ciprofloxacin or other gram-negative antibiotics) and quarantined for an ample amount of time, I suspect that once it's introduced into a tank with other BTAs, they should all be fine. Yet, we see high-end anemones wither away and die.
Withering away is also key--the demise of the sick BTA typically happens so slowly that owners don't notice right away. They also may not notice that the CSB in the tank isn't growing while the other BTAs are growing quickly and reproducing. In other words, they're thriving while the CSB is struggling. That is not indicative of success.
Lastly, yes I've tried it. And I will never try it again. I watched my CSB slowly get smaller and smaller until I had to move it to a QT tank. I eventually had two tanks--one with a CSBs and another with rainbows and purple passion morphs.
It's simply not worth losing an expensive anemone just to attempt to mix them, and be that one person who says "yes, I've done it, I don't understand why you can't do it."