Copyright issues surrounding Lovecraft's estate are insanely complicated. Only a court of law could definitively settle the question, and we are not lawyers. The HPLHS does not speak for the Lovecraft estate. All that said, we firmly believe that Lovecraft's works are in the public domain.
It is true that Lovecraft wrote some offensively racist things and held some very regrettably racist views. It is also true that his opinions changed over the course of his life, and the ugly things he said in his youth were somewhat mellowed by age and experience. But he's been dead a long time, and there's nothing we can do to change him. We can only recognize his flaws, and enjoy those parts of his work that do appeal to us: his fantastical imagination and worlds of ancient mystery. The HPLHS does not subscribe to Lovecraft's racial, political or sociological views, and does not support or promote them in any way.
The HPLHS has a Facebook page and also maintains a number of groups. The largest one is available to the general public, and currently has some 57,000 members. It is a very active place full of interesting and sometimes crazy people who post all kinds of things, not all of which is pleasing or interesting to everyone. There is also a smaller private group just for card-carrying HPLHS members. Only official members of the HPLHS can join this group, and it is more focused in its content. There is also a group for fans of the Dark Adventure Radio Theatre series of audio dramas produced by the HPLHS.