Swiss here that happen to have voted in both polls. I can give you an insight on my view of the topic that may be representative of a part of the population (probably not the majority but at least a significant fraction).
Both initiatives are targeted to a specific extremely tiny population of citizens (most of the trouble is with « converted » Swiss that embrace Islamist views, most of Muslim of foreign origin are pretty well integrated and many even supported the recent burka ban because they know very well what that means) that tries to exploit the democratic system to promote their totalitarian ideology. You have to nip that in the bud. There is for sure some collateral damage as not all people that would like to build a minaret are necessarily islamists but there are prices to pay so that everybody can live peacefully together. The sacrifices will be compensated when the times come.
FYI, back when that was source of troubles Jesuits were banned in the constitution (ban lifted in the 70ties) and some cantons were forbidding to build bell towers for Catholic churches till last century, etc. When the tensions tapered out all the bans were lifted. I’m pretty sure in 50 years if we get rid of Islamism the minaret ban can be lifted with no troubles.
As a side note, by the way it is constructed, essentially everybody in Switzerland is part of some minority and is both paying a bit and getting back a lot in terms of freedom and respect. Everybody depends on the goodwill of the majority so it is in general wary of stomping on other minorities but react strongly when somebody want to destroy the system or doesn’t respect it (most of the sparse cases of real xenophobic behavior, which btw I don’t condone, you may encounter in Switzerland often boils down normal human narrow minds and that).