The source of the conflict is when people from difference set of ideology try to fought, undermine and overcome one and another.
I think that this is often also coming from a pre-emptive defense... from protecting "your own" children from having the risk to marry with people of another religion (or non-religious) and the risk of them being converted.
When for example the people of the Mayflower fled first from England to Holland (the city Leiden). Holland in general tolerant enough for religions, but the parents got worried that their children, playing on the streets with other children, would become likewise tolerant and as "consequence" could "change". => They moved on to the US... in splendid rural isolation. (That they came from a rural part of England played for sure a role as well).
Tolerance as culture, even when not assertive, can still be felt as a threat to more restrictive cultures.
In Holland the issue of tolerance and cultural protection of the various religious streams was "solved" by a "pillar structure" that functioned until the 60ies.
At public level full tolerance, but every religious stream (incl the non-religious) had in my youth its own schools, universities, political parties, youth associations, newspapers, TV, sportclubs, etc. Up to WW2 incl favorable effects on jobs in smaller companies.
It was precisely my generation that started to ignore these borders in socialising. More so in the urban than in the rural areas. And often because of the inflow in urban areas of young people for their higher education.