I think under limited circumstances it will be important. Suppose some is discussing Einstein's theory and was trying to extend that theory, in such a case, reference is required! .Regards.
There is no a fixed format for abstracts in this regard. Some journals accept references in abstract and others do not. It is better to check with the target journal/contact editor before preparing your final manuscript.
I think it depends. I usually use some references in abstract when I use a questionnaire as a tool of data collection. I should say a questionnaire developed by (Hamed,2022) ...... etc.