Honestly, I can't think of an ethical way to suppress the Red Faith if we tried. We can limit its direct, official legal power, but the problem with such a widespread religion backed by its own God is that:
- trying to outlaw it risks rebellion
- trying to limit it too much (no public signs of religion, no religious talk in public life at all, etc) would piss off a majority of the population, including many who are part of our institutions. This is worsened by the complete lack of a good reason we could sell through our nascent propaganda network. To most people, this is normal.
- trying to completely rewrite its doctrine or splinter it risks divine wrath
- trying to give another religion privileges and official powers (ex: only X religion can proselytize or collect official tithes or hold certain administrative or judiciary powers) might succeed in leeching worshipers from R'hllor but would be a step sideways and not forwards.
All that we can really do is hope that our current compromise (all religions theoretically equal, laws and legitimacy are based on our theoretically* non-religious principles, some limits on how openly they can get involved in governing the Realm) works. If it doesn't, we can push and
make it work. If that still doesn't work for some reason, we're sort of fucked.
*This is an increasingly weird fig leaf to have, considering the nascent production of Viserys-Clerics + the Imperial God we intend to develop.