This question is both easy and difficult to answer. Easy because the general directions of the grey areas are fairly simple to identify. And hard because it's not too clear if there are truly distinct "schools of thought" on these aspects, as opposed to conjunctural positions.
Basically the directions of the grey areas are:
Whom does it: public -> private. The more one moves in the private direction the question becomes what is censorship vs. what is legitimate editorial control, or moderation, or simply exercise of private property rights.
A useful reading in this regard, which covers less traditional/recognized methods of censorship such as (economic) media capture is "Selective Control: The Political Economy of Censorship", a World Bank working paper. For a more illustrative but less systematic take see "21st-century censorship" in CJR. Both of these sources cover traditional media, rather than social media. Generally speaking, the higher profile a media outlet has, the more it is likely to experience this kind of pressure, especially under illiberal regimes, under which (sizable) economic actors have a large degree of interest alignment/compliance with the (monopoly) political power, thus to a large extent acting as a proxy for it.
More broadly, there's an obvious tension between private property and (free) speech of customers or employees, which e.g. in the US has mostly been resolved in favor of the property owners. (See e.g. Lloyd Corp. v. Tanner and the MNN case). At declarative level, some international agreements make less of a distinction between private and public actors though, e.g.
the American Convention on Human Rights (which the US is not part to). In the US itself, the NCAC has taken some positions against private censorship, both on art-related and more clearly political issues involving both on-line services and traditional publishers.
If there is (an incipient) "school of thought" somewhat in opposition to that, it may be EU's recent attempts to classify and restrict some actions of "digital gatekeepers". Do note however that the EU angle/concern on this is mostly in terms of competition and transparency though, especially with the DMA. As far as policing speech (DSA), the EU is openly calling for differential rules for the larger (>45 million user) social media firms. But on the other hand, the kind of material that the states themselves can censor is broader in Europe; see below.
The material. It's hard to say here that there is one grey areas as opposed to several. But surely, hate speech (or even blasphemy) is one such topic of relevance to political discourse. (Obscenity/pornography is another content grey area, but less important to the "market of ideas".) Blasphemy laws actually exist in Europe, for instance, albeit not being invoked that often. More national laws restrict hate speech in Europe; see e.g. Wikipedia's summary for Germany. A prototypical example would be (laws against) Holocaust denial--there's also a (2008/913) EU Framework Directive in this area. And even before the recent attempts at codification in the DSA, the EU itself has had agreements with the large on-line firms in this (hate speech removal) area. But not everyone in Europe is happy with this approach; there are activists who have decried all of these and basically would prefer a (US) First Amendment equivalent for the EU countries. (A prototypical US counter example is the Skokie case.)
I'm not entirely sure if this is a proper sub-category of hate speech, but sedition
is another (somewhat broad) category of speech that is outlawed in many jurisdictions, although the exact details differ, sometimes substantially. Although Wikipedia doesn't list it as such, China's
law against inciting subversion is basically in the same vein.
For those with (plenty) time on their hands, the EU Parliament has a (2015) 440-page comparative study on limits of the
freedom of expression in the Union in these two main regards (hate speech and blasphemy, with sedition sometimes mentioned).
Alas even for hate speech, for which there is a EU directive, the study notes/concludes "Member States have not taken a harmonised approach in this respect, thus the list of protected characteristics varies from Member State to Member State."
So, while one could say there's a consensus in the EU on hate speech in principle, there's still disagreement on the extent of what that entails.