How should I respond to full text requests from other researchers I don't know?
Journals have "author rights" policies on what you can do with your paper. (e.g.: https://www.elsevier.com/about/our-business/policies/copyright#Author-rights) 
Most I have seen allow exactly this sort of sharing - at least of the pre-publication draft, if not the final formatted version. 

You should look them up for the journal in question. Even if the policy doesn't allow it, send it anyway. Nuts to journals who try to prohibit one of the fundamental aspects of science. 

(The reason to look it up is to never ever again submit to a journal who has this policy.)