Here’s photo of various flip-flops, borrowed from Wikipedia. The first two in the bottom row I would call thong sandals rather than flip-flops, and those might be OK for Mass, IMO. The pink ones on the top might be OK if they were clean. As for the others, well…if you absolutely don’t have anything better to wear…:shrug:
Yes, it depends on the business. But even in more casual environments, most people would dress a little nicer if they were going to be up in front of a large group giving a presentation, don’t you think? Let us not forget that those who are up front reading/singing/giving a presentation are acting in a leadership position, and it is best for them to set a good example.
FWIW, where I work, the office people are allowed to wear sling-backs or “peep” toes, but not both. Completely open-back shoes such as clogs or mules are forbidden, as are sandals and flip-flops. Those of us “in the trenches” have to wear totally-enclosed shoes, but that’s a matter of safety.