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The phrase "not generally accepted" is correct and commonly used in written English.
You can use it in situations where something is not widely agreed upon or recognized as true or valid by most people. Example: "While some people believe in the concept of fate, it is not generally accepted as a scientific fact."
Exact(58)
However, the method is not free from controversies and still not generally accepted as an acceptable humane euthanasia procedure [1].
Why is catastrophic geology not generally accepted?
"Elderly" is not generally accepted as a noun.
"You have prominent scientists, psychologists and psychiatrists saying this is not generally accepted.
Its elegant, pressed-bow form is based on an engineering principle that was not generally accepted until the 1800's.
"Different imams have different teachings," explained Sue Avery, but "sperm donation for Muslims is not generally accepted.
His central thesis that an exceptional cognitive intelligence is at work in Shakespeare's plays is simple but not generally accepted.
Ader's claims for a second hop of about 100 metres (330 feet) in September 1891 are not generally accepted.
Some aspects of Jewish sexual ethics were not generally accepted among the Gentiles to whom Paul preached.
When I started editing the Guardian crosswords, national identity letters linked to car number plates were not generally accepted as crossword conventions.
These are not generally accepted by historical linguists, who long ago developed but largely rejected a dating method known as glottochronology.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com