The phrase "accepted as equal" is correct and usable in written English.
It can be used in contexts where you want to express that something or someone is recognized or regarded as being on the same level or status as another.
Example: "In a fair society, all individuals should be accepted as equal, regardless of their background."
Alternatives: "recognized as equal" or "regarded as equal."
She said that "to be driving with the Brook family to the seaside and be accepted as equal" was a treasured memory.
He said, "In Islam, Christians, Jews, and Zoroastrians are all accepted as equal — unless they become a Fifth Column for foreign meddling in this country.
The Holocaust convinced many European Jews who survived the Second World War that they could never be accepted as equal citizens in their own countries, that they would always be marked in some way.
"They have put Muslim children from these communities at substantial risk of not being accepted as equal, legitimate and valued members of British society and they have allowed suspicion to be cast on the aspirations of their parents and anyone else who believes that these children deserve the same excellent standards of education as any other child.
"Since women are not accepted as equal human beings but are nevertheless expected to devote enormous energy to the lives of others," she wrote, "the distinctions between their own lives and the lives of those close to them may become blurred.
They are accepted as equal to the 6 classical lines by the Lipizzan International Federation LIFF).
Sadly, to make their mark it seemed to me they were expected by a male-dominated profession to behave like a man before they were accepted as equals.
The treatment of BME judges by our white colleagues demonstrates a culture in which we are not accepted as equals with a fundamental right to challenge discrimination.
They play cricket and football, but in their own leagues, because they feel like they won't be accepted as equals in the mainstream.
For liberal Israelis, and for Arabs who hope to be accepted as equals, Kashua embodied the country's stated ideal of coexistence — of Arab Israelis' full legal and civil integration.
