The Gra saw the energy of spiritual rot of Shabatai Tzvi was subsumed into Jewish cults.
There were many excommunications, but the two points that come up in all of them was disparaging learning Torah and disparaging Torah scholars. Though cults have been hard at work to deny these two allegations by a parade and show of learning Torah, it is still hard not to see that the Gra was right. I do not mean that this is something you can see looking in from the outside, but rather if you are in the actual world of cults it is hard not to admit that both of these complaints are based on actual attitudes that continue today--very strongly.
Now I don't know if it is right to excommunicate people for things, even if they would be 100% true, but the Gra did feel that these were serious issues.
The excommunication of the Gra did not treat this as a minor problem. The actual text stated that one is not allowed to sit in 4 amot [yards] of a chasid, nor talk with a chasid, nor marry the daughter of a chasid etc. It is interesting that this excommunication did not single out secular Jews.
I mean there have always been secular Jews and Jews of various degrees of religiosity. Why not excommunicate Jews that go to Collage? Or other such things? Why specifically Hasidut?
Part of the answer is that the essence of something is what makes it what it is. That is when we talk about the essence of a thing we mean that something else of the same essence would be put into the same category. When there is a claim to be of the same essence as the Creator of the Universe and this does not spark outrage in the general world of , then we know something is off.
The problem of the provability of the connection between Shabati Tzvi with later Jewsih cults was the reason it was not mentioned in the actual text of the excommunication. That was in those days. Today we have lots of evidence of this connection. Cookies that were placed in the writings of the Shatz and Natan from Gaza that you find in all books of Ashkenazic Mysticism. The connection is undeniable. Even if you don't see how that stuff got into Ashkenazic Mysticism never the less it is there.