I know they were in FO1/FO2, but is the brotherhood still "pure human"? Or did they take in a lot of recruits during FO3?

In other words, are the BoS descendants of the BoS is FO1/2 or did they mass recruit wastelanders in FO3?

Which Brotherhood are you talking about? There are at least three chapters that are pretty much independent of each other. The West Coast (original), the Midwest (originally referred to as Eastern) and the East Coast.

Both the Midwest and East Coast Brotherhood chapters originated as West Coast Botherhood expeditions. Both will accept and even actively recruit outsiders, while the original West Coast chapter almost never will. The Midwest Brotherhood may have ghouls, super mutant and even intelligent deathclaws in it along with human tribals (this is open to debate, it is optional in Fallout Tactics but has never been confirmed as canon).

It depends on which chapter were talking about.

For the most part the FO4 BoS seems to keep entrance into their ranks highly selective. I imagine the way our character is brought into the fold is how many are, through sponsorship and invitation.

It should be noted however, that unless they changed this mentality, the BoS believes one of the duties of their people is to procreate. They still probably have some of the purest surface stands of DnA, so keeping those Pre-War genes intact for future generations in an important venture. Hense them discouraging us with fraternizing with the locals. It's essentially a wasted opportunity against furthering their eugenics.

I am talking about the east coast one... Do we know that they mass recruited wastelanders? I read on the wiki most initiates in FO3 would die (high casualty rate). Most of the people we see at the citadel (non initiates) are veterans (pure humans for the west?). If the Arthur Maxson reverted to the older style of BoS, then that would make them more Xenophobic... and thus stop the entrance of wastelands into the BoS. So they'd be mainly pure human... i think?

A high casualty rate would only cause an increase in recruiting activities. The East Coast Brotherhood under Elder Maxson is not xenophobic, at least not in the way the West Coast is. If you check you will find a lot of the people in it weren't born into it.

They recruit Wastelanders, though they are pretty selective (a Wastelander needs to be sponsored by a high-ranking BoS member, like a Paladin). Several NPCs talk about how they joined the BoS. Heck, Danse himself was born a wastelander.

But they are still pure-human because they would never accept Ghouls or Synths into their ranks.

Presumably not and they weren't really anyway. Only those that exist in Vaults, the Enclave, totally hermetically sealed environments for decades after the war can claim that they are.

Even the Institute admit that they are not because they were exposed for some time after the war before they could build their base.