The church I grew up attending, which was built in the 1870s, had a small vestibule where you could buy the Sunday paper or a church calendar on the way out, wain in line for the church’s single bathroom to be free, and where the priest and altar boys could assemble for the processional protected from the rain and snow.
Even at the side entrances there were such rooms (not sure if they would properly be called vestibules, too). As Tarpeian Rock mentioned, this was invaluable in insulating the nave and the people in it, as the holy water in these side “vestibules” sometimes froze.
If they were building it from scratch today, I’m sure they’d have a much larger vestibule for various reasons. But I don’t think the extra set or two of doors has much effect on non-Catholics wandering in. If they’ve taken the leap of coming through the first set of doors, they’ll likely follow the flow of people in to the see the sanctuary. Not only that, I suspect the effect on many visitors is enhanced when the sanctuary is insulated from most of the noise and hubbub outside.