It's corroborated through lore that insurgent/insurrectionist/dissident movements against the UNSC/UEG have had a postwar resurgence in the wake of H3 ("New Blood," and "Bad Blood," novels being the most notable IMO), so it isn't a completely outlandish idea that there could be some militant factions of malcontents actively operating during the time frame for Halo: Infinite.
However, there are a few in-lore factors that strongly indicate to me that we won't be seeing and actively engaging with them during Infinite.
- Insurrectionist means for waging war are limited, especially in the postwar era. I believe the single largest "get" the postwar Innies (at least the faction we're informed on) had was, which through the events of the "Blood" books, they essentially lose as an asset, and which never granted an insurmountable advantage to them in the first place (despite having been a shrewd and potentially very incisive option). In any event, the Innies likely don't have the critical infrastructure to successfully engage in a remote theater of operations like Zeta Halo, even if they could pose a considerable threat to either the UNSC or Banished forces present there (it's likely they couldn't).
- The rise of the Created and the Banished into prominent malicious actors generally opposed to Humanity, regardless of faction loyalty, means that the Innies and the UNSC are backed into a similar corner to that which they were during the early days of the H/C War-- namely, mutually threatened by an overwhelmingly powerful common enemy. Insurrectionist factions would be incredibly foolish to spend military resources trying to fell the UNSC when it is likely that they will, once again, desperately need to forge a protective alliance with them in the face of these new opponents. The possibility of the Banished making an alliance with the Innies, while intriguing on its face, seems like too remote and dangerous a possibility for the Insurrectionist leadership to entertain or pursue. I'm not aware of any serious reason to expect that the Banished would be interested in such an alliance, either, especially considering the very meager gains the Innies could offer them.
That's all Lore-based reasoning, and I stand by it all, but I do think there's a potentially even more conclusive reason we won't be fighting Innies in Infinite.
Microsoft has been concertedly deescalating the amount of mature content in Halo pretty much ever since Bungie left the helm. I think MS's vision for Halo is a franchise that can have the mass market appeal of something like Star Wars. To accomplish this, introducing a nuanced Human opponent in addition to the more clear-cut "Aliens and Space-Robots," fare is counterproductive. A dichotomy of clear good vs evil in the form of a United Human front in opposition to alien factions hellbent on humanities' demise allows for easier and less morally murky storytelling in the mainline games. It's certainly reductionist for MS to go this route when so much of what's made the series so great for so long is precisely the kinds of moral questions it's provided (Morality/necessity of things like the S-II program, etc.), but it is much more marketable to wider audiences- less objectionable to doting parents, more engaging for younger kids, etc.
I think MS and 343i are motivated to minimize the amount of Human vs Human violence present in the series, especially in the most visible and visual mediums (the games). We'll have to see how the Showtime show operates with regards to this to say for sure one way or another, but years of Scholastic publishing partnerships, Mattel and Mega Bloks toy licensing, kids Halloween costumes and pajamas, etc have pretty thoroughly convinced me that it's Microsoft's priority.