One very interesting aspect of LaVeyan Satanism, which most seem to overlook, is that Satan is seen as an aspect of nature, in this case one intiminately related to hedonism, pride, our animistic, base nature. The problem with this is that LaVeyan Satanism is essentially about not fighting our nature, giving into it and submitting certain aspects of the universe. This is, so far as I can tell, the exact opposite of what the WLHP seeks to accomplish, which is a mastery of ones nature, a separation from the greater Nature as a whole. Submission to "forces of nature" is essentially the defining trait of the WRHP.
We also have the issue of Peter Gilmore, a man so dogmatic he believes all who disagree with him "are on some level insane," and holds "nothing but contempt for them." It doesn't take a lot of explaining to show why this may contradict the ideology of the WLHP. Further, the Church of Satan as a whole tens to hold the claim that it is the only valid form of satanism, despite objective and even academic fact disagreeing with this. It may be more an unwritten rule, but when I think WLHP I don't think about denying objective facts just to claim ones sect is the only valid version.