The Center for Puppetry Arts started doing sensory friendly performances about...a year and a half ago, I think. We've gotten to the point where we try to do one for almost every show we do, and even asked some of our guest artists if they would participate, as well. It's been a really great experience for both staff and the audiences. We've even had a number of families come back for non-adjusted shows!
We've found that a lot of the work we do for these shows is managing expectations and keeping everything running on time. All of our shows contain a post-show demo; for the sensory friendly ones, we move that demo to the front of the show. Then we make sure to demo anything that might be startling like a particularly large puppet, or potentially overloading, like a rock-n-roll trip through space with lights, video and the whole shebang. And, particular to us, we have to specifically mention that the puppeteers are there the whole time, even if you can't see them.
We do keep the house lights at half, the doors open, run sound at a slightly lower level overall, and remove any strobes. But that's really about it. For the most part, it really is about giving them a welcoming environment, where they can relax and know they're not going to be asked to leave because their child is "acting up."
On a personal note, we have a family who comes to all of our adjusted shows and their daughter just loves dancing. Any music from transitional scene change music to a big production number, and she is out of her seat, dancing joyfully. I love glancing over and seeing her enjoy the shows, whenever she visits!