The most open is Evergreen State’s BA program, which only requires 180 quarter credits (= 120 semester credits):
https://www.evergreen.edu/registration/degrees
However, most colleges seen as “open curriculum” require at least a major. Some require communication, quantitative, foreign language, seminar, or other course as well. For example, see Amherst and Vassar:
https://www.amherst.edu/academiclife/college-catalog/1718?mmtid=450077
https://catalogarchive.vassar.edu/201314/academic-information/degrees-and-courses-of-study/requirements-for-the-degree-of-bachelor-of-arts/
Note that some colleges like Grinnell, Hamilton, and Smith may have few or no general education requirements, but limit the number of courses taken in one department or general area that can be applied to the degree requirements:
https://catalog.grinnell.edu/content.php?catoid=12&navoid=2537#Requirements_for_Graduation
https://www.hamilton.edu/academics/catalogue/academic-regulations#degreerequirements
https://www.smith.edu/about-smith/registrar/degree-requirements
Rochester and Hampshire tend to be mentioned when “open curriculum” is mentioned, but they have more traditional distribution requirements:
https://www.rochester.edu/college/ccas/handbook/clusters.html
https://www.hampshire.edu/academics/division-i-requirements