I just want to point out that while it is true that there are those that won’t eat Beis Yosef, there are also those who say Bais Yosef is fine but they won’t eat other hashgachos that some of the people who do eat Beis Yosef will eat. And I’m only talking about Ashkenazim here, so it doesn’t have to do with Ashkenazi/Sephardi differences.
There are a wide range of opinions. For every (Mehadrin and Chareidi) hashgacha, you will find some who eat it and some who don’t but do eat the other hashagachas.
That is why you have to ask. That is also why I don’t think this is the place for such a question and why there are L”H issues involved – since it’s not a black-and-white issue and it very much depends on the Rav you ask as well as your own situation.
One of the things that impressed me about the Rav I asked was that his answer was tailor-made for me and my situation. He even told me not to repeat what he said, because it was specifically for me.