[about routing dadoes on finished wood]
If 'finish' is wax or oil or varnish or lacquer, probably it's fine.
If 'finish' is shellac, heating at the cutting edge can cause
it to melt, adhere to the router. And if it's paint, there are some
pigments that can abrade a steel router bit (but probably
OK on carbide).
So, it's not the wood I'd look at, but the router bit, for
gunk or wear.