It would be a LOT easier to find the list of schools using the Profile. There are 3000 or so colleges in this country, and IIRC, about 400 use the Profile.
UVA, University of Michigan, University of Virginia and Georgia Tech are the only public universities I can think of that use the Profile in addition to the FAFSA. The rest of the public universities are FAFSA only.
https://www.nhheaf.org/pdfs/handouts/CSS_Profile_List_and_Assistance_Information.pdf
Scroll down in this link and it gives a list for the current academic year. You do need to check any college website of interest because sometimes this outside info is not accurate or up to date.