I think you are getting hung up on the semantics, stuck on the word "Conservative" you must be confusing "Conservative" American Jews, with Conservative Sepharadic Jews, the distinction must definitely be different, my family are Sephardic Jews, the way they worship is probably MORE biblically traditional than the Ashkenazim as there's been no European influence at all, and there's nothing "reformed" about it.
And since you're being so arrogant about things, I'll throw some arrogance your way, we're more authentic in our practices because we are not Europeanized, that's why we don't wear funny black Fedoras and coats, the requirement for that wasn't mentioned anywhere in the Torah last we checked, and we don't think any of the Jews that left Egypt during the great Exodus were wearing them but you never know, maybe an archeologist will dig up an relief carving of a Jew in a black coat and Fedora hat on old Egyptian column one of these days.
We keep kosher, worship in Hebrew, and follow the law. And most of them are more sincerely Jewish and righteous than a lot of the hypocrites I see out there wearing a Fedora but lying cheating and stealing Monday through Friday, but think they are saints because they go to Shul and keep Kosher? And watch who you call "idol" worshiper, you know a hell of a lot less than you think you do.
From what you describe, it seems you made a mistake by calling it conservative. Perhaps it is "orthodox" but not haredi, and that is the distinction from the black hat culture, but still within the Orthodox tradition's fold.
Maybe that is the case, english was not my family's first language, they originally spoke primarily French, some speak French & Hebrew, and some, get ready to fall off your seat, arabic, Moroccan arabic anyway (plus those other languages). It's wording that's the problem here Conservative - Traditional, it is semantics. Because there's no tolerance of non-kosher or driving on the sabbath etc, in my family or the Sepharidic Jews we know.
Here's the funny part, I'm fair skinned, and have blue eyes, hardly a Mediterranean look, go figure.