Maybe, but wouldn't the same issues apply? After all, you still wouldn't have people going from planet to planet often enough for there to be much interbreeding. In any case, colonizing the rest of the solar system is fairly pointless since there aren't any other habitable planets.
To seriously colonize other planets would presumably mean we've solved the LEO lift problem (elevator? even easier on Mars, the Moon, etc.), have some nuclear-powered shuttles running around the planets, etc. At that point I think there would be at least as much contact between worlds as between continents in the 1500s. It might be largely one-way (Earth to Colonies), though.
Shipping reproductive material (either as information, or embryos, or frozen eggs/sperm) would also be fairly realistic.
The main reasons I can see for colonizing other planets are political (Earth is dominated by a certain kind of nation state, I'd happily live in a remote part of Earth if it would get me out from under that, as long as the right 5k people went with me...), or the spiritual/moral/whatever drive to do it because it can be done.
The fact that no one aside from small scientific installations have colonized Antarctica, which is orders of magnitude more habitable than the Moon or Mars, makes that claim rather doubtful.
