DC has a strong tradition of legacies, so instead of "replacing" a character, they simply introduce a legacy - and in practical terms, they even get to appear at the same time and even share names (we now have six or so earth green lanterns, for example).
DC also has quite a few gay/whatever characters in ther repertorium that people already like quite a bit or are indifferent about, so whenever they feel like they neeed brownie points they can simply bring one of them up (see the general opinion about Midnigther vs general opinion about Wiccan). Hell, rather than create a new gay guy, Orlando outright rebooted Extraño from being a steterotype to being an attractive and competent guy.
Finally, DC has been pretty bad about marketing their diversity characters for quite a bit of time, helped by the fact that media somehow got in their heads that Marvel is the more progressive of the two and everything that DC does is bad. The result is that DC caters less to those types of sites because they know they can't win either way, and try to make their efforts more appealing to "normie" ones, which sounds more genuine in the long run.
DC had a hiccup with the new52 (like replacing obisidian with Alan, for some reason) but they've mostly been corrected.
Marvel on the other hand, thrives on controversy, and they have said several times that their sales method is making people mad. So instead of "we added new Green Lanterns to the roster, by the way they're a woman and a muslim" you have things like "Mar-Vel is DEAD! Read the NEW CAPTAIN MARVEL! If you don't like her you're a loser" because that's what gets them clicks and sales.
It doesn't help that Marvel seems to have no editors whatsoever, so their diversity attempts are plagued with errors, akward writing and subpar art, all a terrible combination.