Yes, Alexander Graham Bell was a eugenicist specifically opposed to deaf people marrying each other (Perhaps a typo in your question?).

He was the chairman of the board of the Eugenics Record Office, served on the Eugenics Committee of the American Breeding Association, was the honorary president of the Second International Eugenics Congress, etc. ^1

In 1883, Bell published a paper called Memoir Upon the Formation of a Deaf Variety of the Human Race. By counting the number of shared last names at schools for the deaf, he determined that congenital deafness must be hereditary, and thus anyone born deaf should not marry anyone else born deaf. He thought that intermarriage would cause the number of deaf people to increase exponentially from generation, and how else did deaf people meet, socialize, and marry than at deaf schools using sign language? So he was an early proponent of mainstreaming as well - don't let the deaf kids near each other, and you won't have deaf marriages. Greenwald has written extensively about Bell's eugenicism; his article on "Upon the Formation" (with Van Cleve) is a very good one. ^2, ^3

So yes, he also wanted to ban sign language, because it gave deaf people a way to be insular and have those deaf kids he was so terrified of. He is known to have known ASL to some degree (probably not fluently), and as a Scotsman in the US he also used the two-handed British alphabet at times, particularly with his deaf mother. But Alexander Graham Bell's name is synonymous with oralism in the United States, and the AG Bell Association for the Deaf is the largest organization for oralism in the world. (They call it "listening and spoken language.") This is because Bell's father invented a method of teaching lipreading called Visible Speech, and Bell used that and his own methods to encourage parents to ignore sign language and use oralism exclusively. ^4

As for how common these views were about deaf people - most of the time, deaf people have been viewed by hearing people as objects of pity, in need of help and "fixing." Deaf people have historically felt they don't need to be fixed, so that is a source of conflict. Virdi's book Hearing Happiness delves into the many, many ways hearing people have tried to "fix" deafness over the years. In terms of how common were the eugenics aspects of Bell's work, I am unfortunately not familiar enough with eugenics in the United States to answer that question. My instinct is that it was primarily a movement aimed at introducing sterilization laws (see the Supreme Court case Buck v Bell [no relation to AGB] for more) and was not necessarily something adopted by most Americans.

Today the impact of Bell's eugenics and oralism is still felt in the deaf community. While this is not exactly the purview of /r/AskHistorians or part of your question, it's worth learning about why he is the "boogeyman of the deaf." Booth has written a book called The Invention of Miracles: Language, Power and Alexander Graham Bell’s Quest to end Deafness; if you're not up for reading a whole book on the subject, she has written this article on the topic, as well.