The CR has several times danced around discussion about the particular Spanish shul in NYC to which I presume you are referring.
Any place that tries to change their minhagim “back to a purer form” of the mesora as opposed to following the contemporary poskim within their circle is bound to become problematic.
Suggestions would include, actually finding a contemporary Sphardi posek to go by, like Rav Ovadiah Yosef, instead of acting like they’re all not truly Spanish enough. If you are referring to the shul to which I think you’re referring, then there probably isn’t a lot of hope. I think they’ve been a stronghold of the Open Orthodoxy/Conservadoxy for as long as anyone can remember.