Personally I would attribute a lot of societal problems to a lack of investment in things that are integral to a properly functioning society.
Ostracizing and excising harmful ideologies is important, but such things don't become problems when there aren't wider systemic problems, like poverty, food and job shortages, wars, lack of housing, underfunded schools/police/etc, lax working safety standards and so on. Nazis and other political extremists don't make headway when things are going well, and the same is generally true of cultural or religious extremist movements. They feed on people who feel alienated and disenfranchised.
For a long time now across Europe a lot of important services have been run ragged by struggling to deal with growing populations and inflation without investment rising fast enough to keep up. Housing and schools in the UK would be my foremost example, maybe police as well I guess. All things that have been struggling to cope with changes for over a decade, but not getting much done for them because the money goes elsewhere, which leaves people in a lot of places feeling abandoned and making problems of poverty and deprivation get worse than they would be if it was caused purely by unemployment.
In regards to interacting with outside cultures and faiths, I honestly would probably deal with them the same way I would deal with the ones already present who have practices I think are bad enough to warrant dealing with. Ban a list of cultural/religious practices and tenets, and exile anyone who practices them. Exile is a difficult thing to do these days, since basically everywhere belongs to someone or is protected from human interference, but there's bound to be some island out there that could be made barely livable and used to dump people on.
As examples of things I would punish in this manner
Any religion/culture that forbids, in text, deed or sermon: exogamy of race culture or religion, homosexuality, transgenderism, polygamy, monogamy, cheating on sexual partners
Any religion/culture that encourages, in text, deed or sermon: the killing of humans(possible exemption for consenting human sacrifice), physical mutilation (possible exemption for consenting adults), harmful irrational behaviour, isolationism, physical violence, verbal violence, proselytization, close kin marriage, arranged marriage (iffy on this one, it's commonly abused, but usually harmless,)
This would probably be a human rights violation, but I do think that it's acceptable for a country to say 'we don't want this here' provided the place they put people isn't significantly worse than the country itself. An island with a bunch of solar panels for power, desalinators for water and some cropland and houses and basic infrastructure wouldn't cost an unreasonable amount for a country to set up and would probably be more humane than prisons are. Probably couldn't support everyone dumped there without major rationing, but that's not something I strictly care about provided it's better than a warzone or a place stricken by famine and disease.
On the tradition subject, I am among those who mostly feel it's a shackle holding people back, but then my own people's culture was actually suppressed by the crown for a long time after some rebellions from the more traditional elements way back. Today most of what I value in my society is less than 70 years old and is embodied by exactly one major political group. I don't give a crap about Gaelic, barely anyone speaks it, I actively view Christianity (and all the Abrahamic faiths to be precise) as an enemy despite having been raised in it, don't care about Burns or Wallace or the old wars between us and England, I have no rose tinted desire to return us to being an industrial nation despite seeing the wrecks of old factories all over my hometown. The extent of 'old' traditions in my culture that I like are my fondness for tartan (iffy on kilts though) and bagpipes, and both of them were outlawed for three centuries. I'm not even going to start on our actively bad traditions like secular violence and rampant alcohol culture, we've only just managed to mostly deal with the former and the latter is proving resilient.