You linked an interview with Childrens' Health Defense, an organization whose primary purpose is to argue, categorically, that all vaccinations are dangerous and do not work. They are the largest such organization and their activism has been directly responsible for the growth in resistance to MMR vaccination and later to COVID-19 vaccination.
This does not mean that the point about a class of antibiotics is incorrect, and I understand that there's a possibility of "strange bedfellows" here because of the potential agreement on the matter of, uh, "big pharma". As I see it, one possibility is that you linked the CHD article not knowing this. Another possibility is that you linked the CHD article knowing this, but figuring just because they're wrong about vaccines doesn't tarnish them on this issue. Another possibility is that you generally agree with their position on vaccines.
I'm not here to judge or change your mind, I'm just telling you that I don't have any prior view about whatever fluoroquinolone antibiotics are. I read the first half of your post wanting to do more investigation. Because of the CHD link inclusion, I am now predisposed not to believe this is a real issue. I am a non-medical social scientist but I have spent a lot of the COVID period publishing work about vaccination. Anti-vaxx stuff is a complete deal-breaker for me. And if your reason for posting was to persuade an audience, I think that's the opposite of what you want.