If it's 25th Century Star Trek, you can bet that you'd see the opposition of some paradigms, the alteration of those models, and some outright iconoclasts of them as well. That's typical in history.
Which means opposition to the Prime Directive, real questioning about the effects of it, as well as surveillance of species.
Television shows try to tie in to the ethos of societal niches, and as a result things like the opposition to surveillance, monitoring of social media, loss of privacy, Big Brotherism, etc would likely appear on the show.
It's entirely plausible for some characters to see the prime directive as a mishappen antiquated model for encountering species, while some may see it as outright evil. Others would cling to it as the foundation upon which Starfleet and the Federation needs to exist.
Think back in history to political and social choices like segregation, seperate but equal, ethnocentrism, considering some sexual identity as inferior or perverse, state religions, etc. We devalue older models over time, discard old ideas, and some folks either vehemently oppose them, or others look upon them neutrally, or others vigorously attempt to maintain the status quo "if it ain't broke...don't fix it...".
An erudite, impassioned, and persuasive revolutionary in some part of the Federation might rally others to his/her cause. It's likely that the Romulans would send aid to foment disorder while they also make peace gestures.
The Federation has never been as militarily powerful as other species. They're so spread thin and lots of Federation races might reconsider their inclusion based upon this movement. In the interim while other species have benefited from shared information, some species may decide the Federation is no longer relevant, or that they might be hampering the success of their species by being a member.
Some revolutionaries (they probably call themselves reformers) might point out the many instances where Starfleet officiers bent the rules, or interpreted the rules, such that the Prime Directive was bypassed. They may see those instances resulting in a more superior outcome.
The deaths of many people within species as a result of noninterference is sure to resonate with the medical profession, as well as humanitarian aid workers, and likely educators.
Disclosure about the Omega molecule, and ignoring or bypassing the Prime Directive may come to light. Someone always talks, and as a starship captain ages, then they are more likely to not be concerned about disclosure. In fact they may oppose that secrecy. This would add fuel to the fire from an entirely different side, and members of Starfleet may begin to also think the Prime Directive needs to be addressed and perhaps reformed.