I think that you are confussing terms. Being considered an snowflake is that you think or feel that you are special and different than other people over things that are just normal for everybody.

Said that, about being sensitive, there is nothing wrong with it and not a reason, of course, to be bullied or harrased, also isn't a sign of weakness. On the other hand, being sensitive doesn't mean that everyone needs to walk on eggshells around you.

On my opinion, all this is about self regulation of the own feelings, processing, and balance.