Gradualmente, entre o 1920 e os primeiros 1960s

Sua avaliação está correta - os mutantes existem há muito, muito tempo, mas houve uma sequência de eventos no século XIX que finalmente os levou à atenção do público. No século XIX, a consciência dos mutantes parece ter aumentado gradualmente, entre o 20 e os primeiros 20s.

O trecho a seguir é da seção wiki do site oficial da Marvel. (A ênfase ousada é minha.)

While records of Mutants on Earth appear as early as 5,000 years ago (with the emergence of Apocalypse in Egypt) the Mutant population did not grow to significant numbers until the early 20th century. Mutant births, however, began to increase throughout the 20th century (presumably due to environmental factors related to industrialization). In 1920, one of the most prominent mutants was born: Namor the Sub-Mariner, who is considered by many to be the first modern-day Mutant. The Second World War saw the emergence of Mutants as soldiers as several...including Toro, the Sub-Mariner, and Wolverine fought in Allied or Axis armies. The World War II era also saw the beginnings of programs which used mutants as genetic soldiers, such as the Weapon Plus program. Mutant births steeped upwards after the end of the war (following the atomic blasts in Hiroshima and Nagasaki).

As Mutant populations grew, human governments and populations reacted harshly to them, and the Mutants began to form widely divergent ideas about how best to live within the larger human society. Mutants broke off into two rough camps...

(Fonte: Marvel.com - Artigo "Mutantes")

Observe que as atividades de Namor eram bastante "públicas" - em pelo menos uma história de origem, ele destruiu navios e guerreou contra habitantes da superfície e geralmente atacou a civilização humana antes de se juntar à luta dos Aliados contra o Eixo na Segunda Guerra Mundial.

Não se pode confirmar, no entanto, até que ponto suas atividades teriam sido relatadas ao público em geral. A resposta provavelmente é "nem um pouco", dado o que encontramos no X-Men Wiki:

Very few people know about mutants before the latter half of the 20th Century...many, if not the vast majority of mutants apparently hid their powers. The general public did know about [supersoldiers] like Captain America. The American military knew of Wolverine, but they were unaware that he was something categorically different from other supersoldiers...Activities of some superheroes and supervillians may have been what notified the general public about the existence of mutants.

(Fonte: X-Men Wiki - Artigo "Mutante")

O problema dos mutantes se tornou um problema nos primeiros 1960s, quando Bolivar Trask, encomendou e criou os primeiros Sentinels para destruir os X-men. A primeira aparição dos Sentinels (junto com Trask) foi em The X-Men #14 (novembro 1965)

• Bolivar Trask was an anthropologist who saw the rise of mutants as a threat to humanity. Bolivar was the father of Larry Trask, ironically revealed to be a mutant precognitive. Bolivar had realized this, and gave his son a medallion which suppresses his power.

• Bolivar is also the father of Tanya, a mutant whose ability to travel through time causes her to vanish but is rescued by Rachel Summers in a far future and become a part of the Askani under the alias Madame Sanctity. Tanya's travels through time would result in property damage to Trask's land. This mysterious situation would only further cement his attitudes.

• Bolivar decides that humanity has to fight back against the mutants and develops robotic guardians for humanity, known as the Sentinels. Larry was shielded from the Sentinels' ability to detect mutants due to the medallion Bolivar had given him.

• Bolivar publishes articles on the threat of mutants. One of these articles showed an illustration of mutant overlords keeping humans as slaves. This illustration would become a symbol for human/mutant relations and several years later Quentin Quire and his Omega Gang would base their appearance on this picture.

No final, Trask sofre o mesmo destino que Frankenstein, para ser traído por sua criação, capturado por eles e observar como eles decidem que são superiores aos humanos e mutantes.

As criações Sentinel de Trask seriam creditadas com a morte de pelo menos dezesseis milhões de mutantes em seu santuário na ilha de Genosha. (REF: X-Force (série 3rd) #03 (2008))

• By New X-Men #115, Genosha had a population of sixteen million mutants and a stable, advanced society. However, the entire island was reduced to rubble and its mutant population was slain by Cassandra Nova's Wild Sentinels. There were few survivors, many evacuated, and the Brotherhood of Mutants turned one of the Sentinels into a memorial statue in #132.

Devido à política de janelas deslizantes da Marvel, todos os principais eventos e personagens são da era moderna. Estamos vendo o 2 do pós-guerra mundial para a maioria dos personagens. O sentimento anti-mutante no 616 é geralmente considerado guerra fria ou mais recente.

Obviamente, considerando que os eventos atuais também acontecem, a equipe principal do xmen é 30ish e agora, 2015. Essa é uma espécie de descontinuidade sem resposta, pois alguns caracteres estão especificamente vinculados a eventos que são realisticamente fora da janela deslizante (tosse tosse Magneto nos campos de concentração nazistas quando jovem) Xavier, por outro lado, continua sendo quarenta anos quando vivo.

Em geral, o sentimento anti-mutante atinge o pico em qualquer idade que a história principal do xmen atual diga. No momento, é mais ou menos o início do 60s do início do 70s.