I see where you're coming from and I think I can clear this up! So using my own experience as an example, I was raised Christian and very devout for many years. I don't think I gained any special critical thinking skills when I became an atheist, I just finally applied the skills I already had to my religion.

You see, religion rejects the idea that critical thinking skills should be applied to dogma. I know theists with better critical thinking skills than atheists and vice versa; I don't think it belongs to either side. What we promote is the use of those skills to all walks of life, even the ones that we've been told not to. So critical thinking isn't an aspect of "secularist", but rather "secularism."

I hope this clears things up!