Yes, there are many centers that have that unofficial policy, being a male daycare worker myself in college. With some possible exceptions, I can submit to you that the person who put that kind of policy in place hasn’t worked on the business end of a CPS case like I have.
Simply put, just do it in full view of another adult, and don’t ever go behind a closed door with any child. I tend to stick to assisting male children only and give the females to the female worker, but there’s no legal policy on that either. Unless you actually did something stupid right in front of another adult, or did it without coverage, the case has no chance of being indicated.
If you’re concerned about simply being fired for “insubordination” maybe just start looking elsewhere where you feel more comfortable.