I was born before the introduction of gender-neutral pronouns, so I understand the confusion that many people feel about them. The pronouns you learned at school were "she/her/hers," "he/him/his," and the plural "they/their," which was used to refer to a group of people.
Nowadays, gender-neutral pronouns (also known as neopronouns) are becoming more common. These pronouns are used to identify ourselves and others without specifically using given names, and they do not specify a person's gender.

Here is a list of some of the most common gender-neutral pronouns:
• They, them, theirs
• Ze/zir/zirs
• Sie/hir/hirs
• E/em/eir
• Xe/xem/xyr
• Tey/ter/tem
• Mx

Recently, I went to a yoga class, and the teacher introduced herself with her name and specified that she identifies as she/her. After class, I left the studio a bit puzzled, wondering if it was really necessary for her to inform me or anyone else in the room about her gender before starting class. Would knowing that she identifies as she/her or with any other pronoun have changed the experience of the yoga class?
Absolutely not.

There are many situations where I don't see the point of specifying someone's sexual orientation, gender identity, or non-gender. Virtual Zoom meetings are another example. Why can't I just learn your name without being informed about if you identify as he/him, she/her, they/them, or something else?
Are we maybe pushing a bit too much with these gender pronouns?

In my opinion, it's important to be respectful of people's pronouns, but we don't need to go overboard. If someone tells you their pronouns, simply use them. And if you're not sure what pronouns to use, just ask. It's always better to ask than to make an assumption.
I wouldn't be surprised if sometime soon the most common question used when you introduce yourself to someone for the first time, "What's your name?", will be replaced with an alternative gender-neutral question such as “What’s your pronoun?”.
I have absolutely nothing against the introduction of new pronouns to be more inclusive, however, exasperating the use of these new pronouns doesn't help, especially not with older people.
I can't even imagine starting this conversation with older people and explaining neopronouns to them.
The problem here, I think, goes back to the basic human need to constantly categorize and label everything, including people.
We like to complicate things when they could be much simpler.
We should all strive to be more inclusive and respectful of people's identities, but we don't need to make things more complicated than they need to be.