Have you ever felt disgust at 'being more sociable' or 'having right
connections' beating the merit?
This sentence is a little bit puzzling, mostly, for me, because of the phrase "beating the merit". But since that is not part of your question, I'll ignore that part and focus on "Have you ever felt disgust ...":
There is nothing wrong, grammatically, with that phrase.
You can "feel disgust", disgust being a noun and the direct object of the verb "feel". And you can also "feel disgusted", where "disgusted" is an adjective (not really a past participle in this case) describing how you feel.
Both of those constructions mean pretty much the same thing, but because "felt disgusted" is more common, if you use the other expression, "felt disgust", it catches the listener's ear a little bit more, and sounds even stronger than the more ordinary phrase ("felt disgusted").
As it is, "disgust" does seem like a pretty strong emotion to feel toward "being sociable" or "having the right connections", but that doesn't make the grammar incorrect. Perhaps "Grammarly’s AI-powered writing assistant" was confused because of the uncommonness of your sentence, and in this case, I think it is wrong. I personally wouldn't put much faith in an artificially intelligent proofreader. Human languages are too complicated for that.
On the other hand, did Grammarly comment on "beating the merit"? Maybe AI is smarter than I think, because I couldn't figure out the meaning of that part of the sentence.
EDIT: OK, after reading your comment, I do now understand the meaning of "beating the merit". I was confused by the way that phrase seemed to be stuck on at the end of the sentence after the two objects of disgust (being sociable and having connections).
If you mean to speak against the fact that "being more sociable" and "having the right connections" are both valued more than an individual's merit, I think it might be clearer if you combined that idea into one linguistic object as the focus of the "disgust".
Something like (for example):
Have you ever felt disgust at the [fact/idea/reality] that
'being more sociable' or 'having the* right connections' [is
more important than/carries more weight than/trumps]
someone's individual merit?
...* It may be regional, but in US English, we tend to use an article with "having the right connections."