No, and nearly everyone who claims that he or she is a "strict grammarian" makes just as many errors as the rest of us.
I've absorbed the rule against split infinitives enough that they sound odd to me, but there's no reason to follow it in most situations. The same applies to ending a sentence with a preposition. Not many people care about trying to make English work like Latin any more.
Errors are one thing, but just ignoring logic in some cases is a whole other thing. And when it actually degrades language and makes it more difficult to use (such as misuse of "literally") then it's a problem.
The stuff you mention in the second paragraph is just dumb though.