I have to disagree. Let aside if it is right or wrong to support homophobic groups. Essence is that many people would hate him for what he did - and I think that it is bad to have CEO who is hated for his personal opinions.
I live in Czech Republic and our past president was global warming denier, he wrote several books about that. I will not judge if he was right or not, but because he had so strong and controversial opinions, it shed bad light on our country.
I think that when you are "public person" or spokesman, you have to be very careful about what you do and say, because then you aren't hurting only yourself, but whole organisation you represent.