I did hang my foam boards. I used double sided tape the first time, it took A Lot!
after a while the still fell down. Then I used the Velcro that has adhesive on it. It worked much better, adhering to the wall, still wanted to come off the foam - I stapled it to the foam board, that made it stay. I haven’t tried to peel the Velcro off the wall- imagining it will probably take the paint like any strong tape, but I don’t think it’s going to cause any real damage.