A number of years ago, I worked for a children's theatre company that did "Sensory-Friendly" performances of certain productions. The house lights stayed on (at a low level) during the show, and certain light and sound cues were altered to be less startling and/or loud.
If I remember correctly, they partnered with a local autism-friendly school and had a pretty good attendance for those performances (they were open to the public, similar to ASL-interpreted shows). One of the parents attending told me about a local movie theatre that did similar matinees.
The most important factor was a friendly, understanding atmosphere- everyone there (performers AND patrons) understood that some children might make noise or need to leave during the performance. Send me a PM if you want me to put you in touch with them.