Obedience has no value simply as obedience. It only has value when everyone agrees with the principles at stake, and agrees they are worth preserving even when it is hard. 

Why would you obey an order you disagreed with coming from a person or entity you already did not like (unless you were in the military or some parallel entity)--assuming this disagreement is based on principle? 

I think you're missing the point. Many people disagree with the Church's so-called theology of sex and gender on principle--in other words, they don't think it's good or worthy of Catholicism--but still love the Church. You seem to denigrate this disagreement as childish or trendy. Perhaps if you gave the dissent its due respect instead of goading people into finding their "secular god," the conversation would improve.