I didn't go to an Ivy league College, but I did go to a Top 10 non-Ivy league and have a Bachelors. It matters to me that it carries weight, because I know when someone starts playing the game of "Who's more educated", my Alma Mater carries enough weight to sink their ships.
College choice does matter, greatly. And in the context of hiring, it matters even more when comparing applicants. Joe has a degree from Clemson in engineering- Cool A+. Dave has a degree from Kansas state Technical institute of wichita- Yea no.
Purely 100% profession dependent. Dr, lawyer, Politics, sure...
In my field, we require new supervisors/managers to have a college degree.... Any college degree.
If a guy walks in that went to Brown, we wouldn't give two shits other than the "damn.. his parents spent waaaaaaaaaaaaaaaaaay too much on college".