I have been composting for years, but have no idea what to do with this. My painters rinsed their brushes into my compost bin.

They didn't do you any real favors, but as long as it was latex, at least they did minimal harm. Latex dries to a plastic material that resists microbial decomposition. At least it should kill anything.

If it's acrylic latex, it probably is a styrene and/or butadiene polymer variant, which yields nitrogen oxide, carbon monoxide, carbon dioxide, and hydrocarbons such as styrene/butadiene as breakdown products. That's quite a bit different from natural rubber latex, but then latex paint is designed to resist biodegradation. (Imagine how much non-degradable paint is used in the world in a year and how many brushes are washed off in kitchen sinks!) Even so, a robust compost pile should do as good a job as any with it. I doubt the amount is large, so I'd probably compost away. The option is to dump it, ultimately in a landfill, which I don't think is a very good choice.