Is it really correct to describe Anders Behring Breivik as a right-wing extremist?

According to his own writings, he is anti-racist, pro-gay and pro-Israel which are not the typical characteristics of right-wing extremists. His opposition to Islam seems to be based on the hostility and violence that many Muslims have perpetrated against homosexuals. His views seem to be very similar to those of assassinated Dutch political activist, Pim Fortuyn, who also opposed Islamic immigration because he saw it as a threat to the liberal culture of the Netherlands.