practice

?Most of the countries practicing multiculturalism nowadays formerly operated under the doctrine of assimilation.

Practice implies a certain set of activities in relation to what you are practicing, and since nothing like that comes to mind in the case of multiculturalism, as opposed to, say, Catholicism, I would use a word like espouse, believe in, have policies of, embrace, accept, encourage, etc. (with slightly different meanings, of course).

Doctrine, too, is a common word in religious contexts (Catholic doctrine), but it is not appropriate here. What about philosophy, guideline, principle, or idea?