Is it safe to allow Adobe Acrobat Reader DC in the Background?

Yes, it is safe. And at present, on Ventura, it is necessary because Adobe has not fully updated Acrobat for Ventura and the workaround is that you have to manually allow the background processes that Acrobat relies upon.

See Adobe PDF reader - Apple Community for more information.

Guy Marino wrote:

Is it safe to allow Adobe Acrobat Reader DC in the Background?

Adobe Acrobat Reader is a popular PDF reader.

https://get.adobe.com/reader/

The choice is yours about "in the background," I don't see how it would be unsafe...(?)

Might draw on resources in the background I have no idea—test it and see. Report back your findings.

I do not use that third party app— however If in doubt refer to the developers website; Support/Help/FAQ/known issues/compatibility/updates/

Contact a third party vendor

Contact a third-party vendor - Apple Support