Technical Writing – How Not to Violate the English Grammar While Trying to Be Gender-Sensitive

This is a grammar error that I see committed by some writers these days:  mixing singular subjects with plural verbs and pronouns.
As a technical writer you would normally never say “He enter their password.” But increasingly, in order not to commit a gender bias, I see documents that contain sentences like “the user should enter their password before gaining access to their account.”
I’m fully aware why the English grammar is bent in that manner and I, a man who considers himself a sincere feminist, totally agree with the motivation behind such trespassing. I have no argument whatsoever with the rationale behind such a rather modern innovation.
But I still can’t help wincing every time I see such egregious violation of one of the most basic principles of the English language. Since rationality and consistency are at the core of technical communication as a discipline, I don’t think I’ll ever be able to make my peace with such a clearly-wrong practice.
Moreover, it’s not like there are no alternatives to the terrible practice. There are actually not one but TWO solutions to the dilemma.
1) SOLUTION 1: Replace the singular subject with a plural subject, and make the necessary adjustments in the predicate too.
Example: “The users should enter their passwords before gaining access to their accounts.”
2) SOLUTION 2: Eliminate all pronouns from the sentence.
Example: “The user should enter the password before gaining access to the account,” or “The users should enter a password before gaining access to the accounts.”
I don’t understand why we technical writers should continue to violate such a basic grammar rule when two alternatives are available to say what we want to say without sounding stilted and awkward.