It is legal to be a bigot, but not on state-funded time using state-funded web sites to promote his bigotry.
He's not promoting bigotry, merely stating he will not write a letter of recommendation. To promote bigotry would be to use the website to attack a religious or racial group for instance. He merely states he will not write a letter of of recommendation to anyone who does not believe in the "accepted" science on this subject. I disagree with the man, but I also support his right to not have to give a recommendation to anyone for any reason.