Is republishing content bad for SEO?

Not if you do it correctly. Republishing the same article on a second site without a canonical tag can dilute rankings — Google picks one version and may ignore the other. But republishing with a canonical back to the original is a standard practice used by every major publisher and costs you nothing in SEO. The bad version is when you republish identical copy across several sites with no canonical and hope all of them rank — they won't. The good version is one canonical original, plus repurposed outputs on other channels that aren't trying to rank in Google search at all.