Can I damage a tubeless rim using a wire bead tire on it? This question is very similar to Can I use a standard tyre on a tubeless rim? but while the answers there set out that it's possible I'd like to understand the risks of doing it.

I recently saw a deal for Fulcrum Red Metal 3 factory wheels that was too good to pass on. Unfortunately only a couple of weeks ago I stuck a new pair of Maxxis Igniter wire beads on my bike. The tyres are cheap but I like them and wouldn't mind keeping them. Is there any risk of damaging the new rims if I run the wire bead tires with tubes in them? Also is there any risk of damaging me?

They have a big Only Use UST Compatible Tires sticker on them so thought prudent to ask. Not worried about any liability issues New Zealand has a national no fault accident insurance scheme which covers personal injury.
To answer your question in a word: No.
You can run any tire on the rims you want. The "UST only" sticker is referring to when you're running tubeless. Even then I wouldn't pay it much mind. There are plenty of good non UST tubeless tires out there. Squirt some sealant in there, air them up and off you go. The UST standard is a dying (dead?) standard. Our friend Stan played a big part in making that happen. Before there were many tubeless tires available his tubeless kits converted most, but not all, non tubeless mtb tires to tubeless with no more issue than you would have with a UST certified setup. Some would argue that the NoTubes kits were more dependable than UST.