I'm going through some older code and there's a lot of .gt.'s, .lt.'s, .ne., etc. That's fine for me, but are these considered obsolescent? Should I be replacing them with <, >, /=, etc. to keep our code base up to date, or is it totally a preference thing?
No, they are not deemed obsolescent. It's a style preference. I will use the symbols in new code, but would never consider changing them out "just because".
In general, I am opposed to rewriting code just to keep it "up to date", as this raises a serious risk of adding bugs. "If it ain't broke, don't fix it" is my motto.
(For what it's worth, I am the convenor (chair) of the international Fortran standards committee.)