It works at first to just always use names and theys, but the longer a conversation goes on, the more awkward little nooks and crannies you find where it sure would be convenient to have a third-person singular pronoun for referencing the thing the person just said as you expand on it or synthesizing between statements made by multiple other participants. Maybe each one individually has a solution, but the cumulative effect of these small hitches and inefficiencies does build up.
Anyway, it's not impossible to make this feel natural, of course, and some people put in the work to master it. But there's a reason To Kill A Mockingbird stands out as a book that almost completely conceals the gender of its narrator and main character until about halfway through the story.
As another commenter pointed out, in a professional setting you would ideally address these people by their proper nouns (names) and not by their pronouns. And if you're addressing more than one person, it's the gender-neutral we/they/them anyways.
I'm actually struggling to think of a business scenario where using the proper pronoun would be more professional or polite than just using someone's given name.