singular or plural? The whole of A & B is/are?

Solution 1:

There are actually two factors here:

1. Modifier ambiguity. You're correct that "whole" can be interpreted as modifying either both "society and the religious world" or only "society". However, the natural interpretation (in my opinion) is certainly the former. To say the latter I would explicitly prefix the sentence with "both" ("both the whole of society and the religious world"), in which case "are" is certainly correct.

2. Collective noun. Is "the whole of society and the religious world" being treated as collective noun? In other words, is the impact described happening to the members of society or to the structure of society itself? If it's the former, then it's normal in British Englishto use a plural verb despite the grammatical singularity of "whole of"; otherwise, you should use a singular verb. In American English, meanwhile, a singular verb is expected in both cases.
   
   This point is best illustrated by the two sentences "My family is big" and "My family are big". In British English, the former would imply that you have many family members while the latter would imply that those family members are obese. In American English only the former would sound grammatical.

Solution 2:

I would suggest using was/were in the following manner:- 1) "the whole of society" and "the religious world" were strongly impacted by this new religious view.

2) The whole of "society and the religious world " was strongly impacted by this new religious view.

However, I would like to reconstruct the sentence as:-

Both the religious world and society as a whole were strongly impacted by this new religious view.