Animacy, not Gender
If you don’t know what someone’s gender is, you cannot call them an “it”, for “it” is not about gender. It is therefore ungrammatical in English to use its to refer to a human being, whether you know their gender or not.
That's because it is not some sort of marker of gender in English but rather a marker of animacy — that is, of agency and sentience. The Wikipedia article on Animacy observes that:
The distinction between he, she, and other personal pronouns, on one hand, and it, on the other hand is a distinction in animacy in English and in many Indo-European languages.
So it turns out that the issue of “animates-vs-inanimates” trumps the
“battle of the sexes” in English. Here are some examples:
If you say that everyone is wasting your time, that means that you are the one whose time is being wasted.
If you say that everyone is wasting my time, that means that I am the one whose time is being wasted.
If you say that everyone is wasting her time, that means that she is the one whose time is being wasted.
If you say that everyone is wasting their time, that either means that they are each one of them wasting their own time individually, or else that there exists some group whose time is being collectively wasted (which may or may not match the subject).
You cannot use it for people. To do so is confusingly ungrammatical or offensive, or both.
Here from the Wikipedia article on English personal pronouns is a simple chart explaining this: