I think it is perfectly reasonable for a RO to say 'if you want to enter this race you must pin your number unfolded on your chest so we can easily read it.' If this means you have to wear a vest then wear one. If you don't want to do that don't enter the race.
If you are going to have a rule you have to be able to enforce it and the best way to do that is to say if you don't comply with the rules you are not in the race and considered a side runner, therefore your name will not appear in the results.
It is hardly a hardship, in bad weather I unzip or lift my top so marshals can see it as most of us do. I think of it as a common courtesy to the people who are giving up their time to do this for us.
Mark -current FRA member