It also depends on the league/rink as well. Living in CA, AZ, WA, and NV I have seen some associations that don't care at all while others require at least a half shield.
This is also the same with shoulder pads, most of the associations didn't care at all, but some of them would immediately remove you from the ice if you tried to play without a chest protector of some type. I assume those associations has some type of incident occur, and they implemented those changes due to insurance or legal reasons...?