@ NCB
Eg. the fact that Litvish yeshivas don’t have mikvahs b’shittah, the fact that litvish bochrim are clean-shaven b’shittah, the fact that litvish bochrim could go years without saying korbanos b’shittah, etc.
None of the above are examples of playing fast and loose with Halacha. Mikvos, beards, and saying korbonos are not mandatory m’icker hadin.
There are times when a pre-existing, widespread practice seems to contradict Halacha, and it can be shown that Rabbonim were aware of the practice, and didn’t object to it. THEN, based on the above evidence (widespread practice w/o objection) subsequent Rebonim may propose a solution. Such a consideration is itself very much a part of the Halachic due process. And even still the proposed solution may well be rejected by Rabbonim who are contemporaries of the Rav who proposed it or the Rabbonim of subsequent generations.