I don't know about weird laws in WA, but I can give you some general advice.
Some types of people absolutely would use your poly lifestyle as ammunition in a legal battle. Slut shaming is really prevalent in child custody battles. Someone who wants custody your kids is going to try to paint your lifestyle as unstable and unsafe. There are three overarching things you'll have to prove to be able to keep your kids, no matter what state you're in, and those are (1) your environment is safe, (2) your environment is stable, (3) you have parenting skills.
The best way to be able to prove these things is to document everything you do for or with your kids. Keeping a separate calendar for that stuff. Extracurricular activities? Document it. School meetings? Document it. Grounded a kid? Document it. Have you attended parenting classes? Support groups? Document it. Take them to the doctor, dentist, etc? Yup. On the calendar. Also note down everything that you know that your ex-partner does (or doesn't) do. "I always take them to school!" is a lot less convincing than "I took them to school every day for five months except one day Ex took them. Yes, I'm 100% sure because I keep a calendar."
Have you done a background check on the person you're moving in? If you haven't, you should. Not because you don't trust him, but because if it comes up you can say you were proactive in keeping your children safe. That you did a background check is proactive, verifiable, and a lot more convincing than having a friend come in and testify that you are totally a good parent.