It's already tacky to have included any registry information - it's telling people where you have pre-selected your preferred gifts. Anyone who wants to know will ask when they RSVP. It literally takes 10 seconds to ask or 30 to find it online.
I disagree, for a shower I prefer to have the registry information. I am going to the shower with the intention of buying a gift for the MTB and it makes my job easier, as a guest, to have the information included. Lots of times, I am a last minute shopper and if I don't know where the MTB is registered I won't ask and end up getting clothes or something I think is cute. On a formal wedding invitation, then yes its tacky, on a baby shower invitation I think most people have come to expect it anymore.