I don't see why adult X-Men can't fly under the radar as far as the Avengers are concerned. A couple reasons:
1) Up to this point, the "mutant threat" has likely been pretty negligible, mostly focusing on the occasional flare-up with Magneto. And if they write a Magneto who has a mutual interest in keeping the existence of Mutants quiet, then that works, as whatever plan he enacts would necessitate avoiding drawing attention to the existence of mutants. It won't really come to the forefront until, as I suggested earlier, you have rogue government agents hurling Sentinels in public, or someone like Mr. Sinister, Apocalypse, or Stryfe coming on the scene with a vested interest in kick starting a war between mutants and humans. Otherwise, you have the X-Men, Magneto, the government, the Morlocks, etc. all invested in the idea of keeping the existence of mutants under wraps.
2) The Avengers aren't aware of all super-heroic activity. They seemingly never heard of Ant-Man or Captain Marvel, after all. Captain America and the rest of his team were taken totally by surprise when Spider-Man showed up (Tony seemingly being the only one who knew about him). And nobody was aware of the existence of Black Panther or the true nature of Wakanda. So a handful of superhumans who occasionally get into fights with another team of superhumans could easily slip under their radar. Particularly if the battles occur in out of the way places rather than the middle of Manhattan (I.E. Asteroid M, the Savage Land, Alamogordo, etc.). And if the X-Men and Brotherhood are currently living under a "détente" scenario, then it's even easier.
That, I think, is the best option for Marvel. It gives them an X-Men team which is relatively young, in their mid-20's, but still somewhat experienced. It gives them established background with their most common archenemy, Magneto and his Brotherhood (Meaning that if they ever make a movie, they don't have to establish the relationships between a dozen or more characters, because they can write them as if a relationship already exists, and every character is well aware of who everyone else is and what they're capable of). It sets up the framework for why mutants continue to remain secret, because the X-Men have been there enforcing the secret, working in tandem with the government. It allows for a POV character to be introduced to the X-Men, similar to Rogue and Wolverine in the first X-Men movie, to introduce us to that world, rather than having to build the entire world from scratch. And it allows for a younger generation of students in their teens who could be the basis of a very different kind of film series. One which is more Mutant Harry Potter than anything else.
At the same time, they're still young enough and new enough that a lot of their enemies have yet to arrive. No Mr. Sinister and the Marauders. No Apocalypse and the Four Horsemen. No Stryfe and the Mutant Liberation Front. No Purifiers. No Reavers. No Hellfire Club. And so on. X-Men with 10 years of history behind them is, in my view, their best bet.