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The phrase "are allowed to exist" is correct and usable in written English.
It can be used to indicate permission or acceptance for something to be present or to continue to be present.
Example: "In this community, diverse opinions are allowed to exist without fear of judgment."
Alternatives: "are permitted to exist" or "are authorized to exist".
Exact(25)
There is nothing showy, nothing overstated; the pictures, like the girls, are allowed to exist quietly in their space.
Hence, in effect, no waves or wavelets are allowed to exist outside the geometrical light beam defined by the rays.
The boycotts have largely been the effort of individuals and small groups without government involvement, like student organizations and such civic organizations as are allowed to exist.
Even if private prisons account for a relatively small proportion of the prison population, that they are allowed to exist at all is an indictment of our system.
It is regrettable that Hitlers are allowed to exist; but universal freedom is a higher good than the release from local pain.
As long as too-big-to-fail banks are allowed to exist, they will be in a position to extort the government and the taxpayer in a crisis.
Similar(34)
With expenses, an ambiguity was allowed to exist between allowances ("just divide the maximum into 12 monthly payments," MPs were told in the 90s) and out-of-pocket expenses.
The caliphate has survived its first year of existence, and as long as it is allowed to exist in Syria, it will continue to expand, both there and abroad.
"The terrorists should not be allowed to exist at all.
If the stuff is allowed to exist, it will stand.
When you think about it, it's surprising that art is allowed to exist.
More suggestions(18)
are allowed to implement
are allowed to list
are permitted to exist
are allowed to practice
are allowed to survive
are allowed to happen
are allowed to apply
are allowed to emerge
are allowed to establish
are allowed to need
are allowed to occur
are assumed to exist
are expected to exist
are reported to exist
are considered to exist
are able to exist
are supposed to exist
are allowed to persist
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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