no one cares. Right wingers try to make this pronoun stuff seem more important than it is. If you're keen that people know your pronouns- mention them. They are not gonna indicate anything about your political leanings or your class status or anything. If you don't mention them, people are not gonna think you're bigoted, they're not gonna think anything at all. they will think you're awful if you fail to behave like a decent person and insist on addressing people with their gender assigned at birth instead of their stated preferred pronouns.
No one reads your CV that carefully to notice whether or not pronouns are mentioned/ not mentioned. recruiters usually are looking for whether you've got experience and education and can demonstrate required skills.

These days it is a good idea to write your pronouns as much as possible. These days your CVs are less likely to be read by boomer alumni of traditional universities and more likely to be read by NLU alumni who are younger and more sensitive to social justice issues. In another 10 years it will be the norm.

“To make a good impression” - Heck no. Nobody who is working in a fast paced environment like a law firm gives two shits if you're a he intern, she intern or a they intern. Even otherwise, why is everyone so into flashing their gender with their names like some sort of a disability certificate? Or is it pride? Yay, I'm a she. A she who works crowd goes wow.
Aren't all genders equal? - I believe they are.
So why do people get offended if, by mistake, someone addresses you as a he/she the first time you correspond/speak.
I'm a girl. I don't give a shit if someone calls me a he the first time we correspond/speak. I will correct them politely. I don't think anyone’s so forgetful that they will still call me a he. Again, even otherwise - Who gives a shit?

How does writing (he/him) shows you belive in equality?
If anything, I think it shows you don't belive in equality. You're more likely to have a soft side for LGBTQIA+ community and therefore a bias, thereby removing the scope for equality.

Stop the vitrue signalling. If you actually belive in equality and inclusion, show it by your actions and not changing your IG bio.

I see many alumni of top NLUs in law firms write pronouns next to their names on social media. Is it recommended to do this for students while emailing such people, to make a good impression and show that you believe in equal rights for all despite your masculinity and privilege? However, most of the people I see specifying their pronouns are woman writing "she/her". I rarely see men writing "he/him". Should guys still do it or is it only meant for girls?