Imo, no, they aren't LGB. A big part of the gay liberation movement was getting people to be comfortable with the idea that some men have sex with men and some women have sex with women and bi people have sex with both. A lot of the issues of the LGB movement evolved from sex (ie. the idea of men as bigamous sexual deviants, straight men fetishizing lesbian sex, ideas of gay people as sexual predators, etc.). We have since moved on to more second and third order issues (ie. marriage, adoption, employment, housing, etc.) but almost all of those issues still included sexual elements (consumption of marriage) or are objected to based on sex (ie. adoption and child abuse). So no, the issues LGB people and asexual people face (I frankly don't even think asexual people face that much opposition) are nowhere near the same. They only appear to be similar at an extremely surface-level view. Edit: for clarity. I am not saying LGB people have to have sex. I had zero sex in my first relationship, but we were not asexual nor did we call ourselves asexual. Imo, the presence of any sexual desire in a person's life undermines the idea that they are asexual.