the majority of people allow their opinions to be swayed by a minority of individuals.

I don't see how to make predictions from this or easily modify it to be able to do so. Note that every majority opinion consists of slightly different opinions that are each minority opinions.

My intuition is that people have different thresholds of agreement around them to hold each opinion they have. If 60% of people are at least comfortable holding an opinion so long as at least 50% hold it, and a subset of them, at least 50%, are comfortable holding it so long as at least 40% do, etc., the belief will be stable.

But if support for an opinion is shallow and fragile, such that some people are only comfortable holding it if it is nearly universal, and others only if it is overwhelmingly popular, and others only if it is a supermajority opinion, etc., support for it could unravel quickly even if people change little.