This is a great question, as the 20th century saw the most rapid change for the public perception of Deaf community for several reasons. The most obvious is the advent of new technologies, but also cultural and linguistic factors.

As my expertise is specifically focused on the Deaf community in the US in the 19th and 20th centuries, that's where my answer is going to come from. To some extent it can be extrapolated to other countries, most closely Canada, but also some countries in Western Europe whose cultures parallel the US most closely.

Let's start with the early 20th century. The 1880 International Congress on Education of the Deaf, in Milan, saw most educators deciding that sign language was bad and speech was good, because (they said) deaf people should be more like hearing people.^1 As a result, schools around the world stopped teaching in sign language, including many state schools in the US.

Because so much time began to be spent on speech therapy, many students lacked a well-rounded education. Vocational education was considered important^2 - preparing deaf children for a trade, rather than university, because that was "all they could do." Public perception was not unfavorable, exactly, but deaf people were thought of as objects of pity, not societal equals, by hearing people. There were certainly standouts who were lauded by their communities for their success in a particular field, but by and large deaf people were seen the same way most disabled people were seen - as inferior.^3

(I should note that the deaf community did not see itself this way. Deaf people had just a strong and robust community, including national and local events organized by social clubs, the National Association of the Deaf and its chapters, and the National Fraternal Society of the Deaf and its chapters. Deaf people did just fine as an insular community with a shared language - but the question focuses on public perception, not internal perception.)

The perception of deaf people most likely began to change around WWII. Many people are familiar with Rosie the Riveter, the symbol of women who took on factory jobs when men went off to war - but deaf men and women (who of course could not serve in the military) began to work in factories as well. Akron, Ohio already had a number of deaf workers at the Goodyear plant^4 (they had their own football team, the Goodyear Silents) and elsewhere, and during WWII Akron blossomed even more - the American Athletic Association of the Deaf was founded there in 1945. Working alongside deaf people, and playing sports against them, helped hearing people see deaf people as capable fellow citizens.

In 1960 we get a bigger improvement, but it takes much longer. That's when William Stokoe, a hearing linguist, published works identifying American Sign Language as a real language, not pantomime.^5 (He worked with Dorothy Casterline and Carl Croneberg, deaf researchers, but Stokoe usually gets all the credit.) Stokoe's research put in motion very slow changes - at first, even deaf people were resistant to the idea that sign language was a natural language, because they'd been told all their lives that it was inferior (and even that it could not express abstract thoughts like love!). Ongoing research in the 60s and 70s led to the acceptance of ASL as a language, and in the 80s and 90s it became popular for hearing people to take sign language classes too.^6 The status of ASL as a full and complete language isn't necessarily understood by the general hearing population, but it is typically acknowledged to be "as good as English" which is good enough to help hearing people see deaf people as more equal.

Technology in the 1960s and 1970s begins to level the playing field for deaf people even more. Acoustic couplers and teletypes, originally adapted by James Marsters and Robert Weitbrecht, made it possible for deaf people to use telephone services.^7 Relay services, which began in 1974, made it possible for deaf people to call hearing people on the phone. This wouldn't make things as equal as you'd hope, as early services were very slow, but IP relay (via computers) and video relay (for sign language users) have helped eliminate a lot of this issue. Getting a relay call still frustrates some people, but they tend to be more frustrated with the technology than the person.

So all of this sums up to a much improved view of deaf people by the hearing population. I'm speaking in the most general terms, of course - there are still awful people out there. But enhancements in communication and increased exposure to deaf people (including through mainstreaming of deaf children in hearing schools) have led to most hearing people treating deaf more as equals rather than objects of pity.