Problem with real SHIELD is... they are fanatics.
Letting aside the fact that all theyre valid points tend to forget the also valid points of all the MUCH of what Coulson did right, thats theyre basic problem. They are absolutists.
I understand them. I do. They saw friends die and betray them, they saw theyre lifes meaning (we have seen Bobbi´s believe in SHIELD as a life mission in several episodes before) crumble to ashes, and in one moment were an order by Fury seemed just to tell them to see more of theyre friends and companions die, they realized, from theyre point of view, that it was Fury and his way of running SHIELD that was to blame, and they swore to rebuild SHIELD to work in a way diferent than before, so that that horror would never happen again. To them, Coulson, a continuator of Furys way, with all his good intentions, is just re-building the same trap that will fall apart in the future. They cant allow it to happen again. They just cant. And they wont allow it.
I understand that. The problem is... a fanatic is a fanatic. And that never ends well either. True SHIELD cant really ask for much simpathy from the moment it calls itself TRUE. They dont discuss. They dont negotiate. They dont inform. They tell you that you are wrong. Its theyre way, or the highway. If Coulson is a good man, he will understand why we had to do it, if he disagrees, well, Bobbi, then he wasnt that good of a man, was he? Gonzalez didnt come to debate, he came to show you the true light. It never ocurs to them that there might be several valid ways to run SHIELD, or that they might just be wrong. They didnt try to improve Coulsons SHIELD, os asimilate it. No. They just obliterate it and told him "Sorry, Phil, you are out of business. Your opinion? We dont care.".
Its a revolution, and as with many revolutions before and after, instead of just achieving the well deserved freedom they got, they start to take dissenters freedoms away in the name of not loosing the freedom they got. Unlike real revolutions, wich usually are started by people with alredy rotten hearts, this people have theyrs on the right place. Unfortunately, for an organization that had its EUREKA moment when they realized that they could be run in a more democratic way, they are, diferences aside, acting very much like fascists.