Important points! Root cause is that there is no clear bounds on “faculty” and no theoretically defensible measure of individual ideology. Best it can be is a proxy for the universe of ideas considered and debated on campus which is the right concept to care about.
There is no such thing as a perfect measure of faculty ideology.
Surveys: low response rates, social desirability
Twitter follows (i.e. Barberá 2015): many academics have left the platform
Donations: many faculty don't donate
So any measure needs to come with, at minimum, very serious caveats.