It's bad enough that it splits three infinitives with that colon there, but each of the things it's asked of us not to do starts with "not". If you're going to factor out the "to", factor out the "not" as well! That would make the bit up to the colon read "It is asked of you to not:", or, better, "It is asked of you not to:". Don't they teach algebra in schools any more?
Personally, I'd have gone with "It is asked of you not:" and then have "to damage items", "to shoplift" and "to be rude", mainly because it's unimpeachable grammatically but would somehow irritate everyone who reads it.