No there's generally no comparison, it can go to far sometimes for some people and has resulted in a few deaths and suicides, but it doesn't equate to the bias gay or black people face. Wiki has a bit on it though:-
''A UK woman recently won an award from a tribunal after being sexually harassed and receiving abuse because of her red hair;[58] a family in Newcastle upon Tyne, England, was forced to move twice after being targeted for abuse and hate crime on account of their red hair;[59] and in 2003, a 20 year old was stabbed in the back for "being ginger".[60] In May 2009, a British schoolboy committed suicide after being bullied for having red hair.[61] The British singer Mick Hucknall, who says that he has repeatedly faced prejudice or been described as ugly on account of his hair color, argues that Gingerism should be described as a form of racism.[62][63]''