They have been trying to scare folks for 50 years about this. If there was any real issue, we prob would know about it by now.
%%I remember having this discussion in my college biology class decades ago. Since sweating is a normal process in the body, the instructor told us that antiperspirants were potentially unhealthy because they blocked or in some way suppressed the release of sweat. But a lot of people use antiperspirants and you don't hear about a lot of health problems, so maybe not so bad.