What Is The "Church" Under Protestantism?

 What is the Church in Protestantism? A common answer is that it is like an invisible fellowship of believers. So if Adam, Bryan and Chad gather for worship and some Bible reading, that is a microcosm of a church. Small, sure, but still a church gathering. Contrast this with something a bit stronger, which claims a visible church. An institution which exists that has defined rules for membership like the sacrament of baptism for example. What are the defined rules of membership within Protestantism? It doesn't seem to have a good answer for this. 

Take their common answer that it is an invisible fellowship of common believers. There are two red flags to be raised here. First, how do you defined what it is that is needed to believe? Second, what is it that does that if not a visible institution? So suppose the Protestant says you need to believe in the Trinity, and so a church is a fellowship of Trinitarian believers. Okay, first, why is it that the Trinity needs to be believed. To be sure, I don't deny that it does, but under Protestantism, what makes that the case? Was there a council like there was for us? I mean, you look at the Southern Baptist Convention right now and there seems to be a hesitation to adopt the Nicean Creed. 

Take this analogy. Universities are visible institutions that have well defined parameters to be a student or faculty. This would be akin to the Catholic Church. Protestantism would be like a meeting of communists out on the quad. It would be a meeting of like minded ideologues, but nothing coming close to the formality of the university. And there seems to be something necessary to that formality. Like the ability to dish out discipline, and correspondingly, church discipline. This seems to be a problem for Protestantism.