I used to use HDPE soap molds years ago. While they didn't stain for me, I found it hard to unmold the soap. The molds came apart; but the sides and ends would often stick to the soap. They may have improved since I used these kind of molds.
I have not had an issue with staining in my HDPE mold and I have had it for about 10 years and bought it from another soaper. I use strong infused oils and no issue at all for me.
I don't have a problem removing my soap from the mold either but the soaper that sold me the mold did so for the same reason as lsg had. It appears to be a recipe issue and luckily for me mine works.