For a player it's not necessary to read the whole book.
It is polite, however, to at least go through the section about their character.

I'd still skim the rules in that case as well. It would be the polite thing in my mind 😅

The role does matter.
But even for lite games I would probably skim the rules a bit. It would feel weird for me to just go in a session without having any idea of how things work, mostly because I wouldn't want to bog down the game for the rest of the group.

That makes sense.
I only go cover to cover on rulebooks that greatly pique my interest design wise

I have had players in my group who had never checked out a Player's Handbook, but only a few of them and most of them quit.

Technically you don't need to go over all of it. I wouldn't go over the spell section of the D&D Player's Handbook spell by spell. But as a GM I would probably have to check out more parts than what a player would have to.

The majority of the people there, said they usually check out the rulebook, even if it's only for the section related to their character and some general rules.

Having someone who already has an understanding of the game is always good. That goes for all types of games.
In many cases I'm that person, especially in RPGs since I want to try new ones every now and then 😅

That's my thought as well, but I tend to like books a lot.
I learned others don't want to check out the rulebook. Well, as long as they don't cause an issue in the group, that's fine by me.

Glad we helped! 😁