note: i do not fw the author stephenie meyer - see below
jasper, one of the cullen siblings, was originally a confederate soldier. for anyone not from the u.s., the confederates were a political group of southern states who, in the 1800s, tried to secede from the rest of the u.s. for the primary purpose of upholding slavery. so jasper being an ex-confederate isn't great, to say the least. to make it worse, stephenie described how jasper lied about his age in order to enlist early. so this is not some failed attempt at complexity, where jasper might've been forced to join for some reason - stephenie specifically and purposefully emphasized how much he wanted to join. on top of that, jasper never once expresses any regret for fighting on the side of slavery, even when he's recounting his experience to bella in eclipse
the quileute tribe is currently trying to relocate to outside a tsunami zone: donate to the move to higher ground project here
the werewolves in twilight are all from the quileute tribe in la push, washington. not only does stephenie meyer completely misrepresent their faith and beliefs (especially in relation to wolves and ancestors), she refuses to give them any profits that she's made off of twilight. additionally, she portrays all of her indigenous characters as inherently more aggressive and angry than her white characters, which is obviously a racist stereotype. notably, the leader of the werewolves, sam, is a domestic abuser who permanently disfigures his wife because he "couldn't control his anger". also, a lot of the indigenous characters come from broken families. the older ones explicitly prey on younger girls (see: imprinting). all of these are racist stereotypes about indigenous people, and stephenie meyer includes them shamelessly.
there are very few non-white vampires in the twilight saga. in the first movie, the director catherine hardwicke wanted to make more of the cast non-white but stephenie meyer literally fought her every step of the way. hardwicke was barely able to include edi gathegi as laurent. this is because, in stephenie's lore, becoming a vampire sucked all the pigment out of your skin. this point has been made before (see linked videos below), but this idea that vampires are pale because dead people are pale is very white-centric. when white people die, their skin gets a lot paler. however, that doesn't really happen as much with people with darker skin tones. anyway, stephenie meyer used this to argue that basically all vampires are light skinned...
in breaking dawn part 2, the cullens are going around the world being introduced to a bunch of different vampires. two of the vampires they meet, senna and zafrina, are amazonian, and the way they're portrayed... it felt a little exoticizing
if you want to see race in twilight discussed more / more in depth:
basically, i think engaging with twilight is fine as long as you acknowledge everything i addressed above and don't shut down discussions or criticism of the racism present in it. this belief is strengthened by the fact that stephenie meyer is very explicitly not a public figure - unlike j.k. rowling for instance, she isn't really relevant and doesn't have the ability to cause more damage (other than what she's already done)