What is wrong with free-thinker? Does it connote more emphasis on atheism as opposed to rationality in general?
Huh. Now that you mention it, I don't know... it mostly just feels outdated, I guess, which is not in and of itself a reason to discard it.
I feel that the term "rationalism", as opposed to "rationality", or "study of rationality", has undesirable connotations. My concerns are presented well by Eric Drexler in the article For Darwin’s sake, reject "Darwin-ism" (and other pernicious terms):
So, my suggestion is to use "rationality" consistently and to avoid using "rationalism". Via similarity to "scientist" and "physicist", "rationalist" doesn't seem to have the same problem. Discuss.
(Typical usage on Less Wrong is this way already, 3720 Google results for "rationality" and 1210 for "rationalist", against 251 for "rationalism". I've made this post as a reference for when someone uses "rationalism".)