> "Don't consume chemical sweeteners" is a pretty good rule of thumb.

I assume you mean non-caloric sweeteners, since all sweeteners are chemicals including table sugar (sucrose).

While suspected, few have any proven negative impacts. AceK and aspartame are probably the most well studied and the evidence is equivocal. It's probably in the end net neutral.

Some even have benefits, including most sugar alcohols being good for oral health. Erythritol has antioxidant effects in animal models as well.