If "variety" is a singular collective noun, can I refer to it with "it"?
No, it's not unambiguous. It can be referring to either a variety or to shop vendors including a variety.
(My personal parsing would be to interpret it as referring to the action rather than to the noun, but that's subjective.)
To rephrase it to make it unambiguous, you have to drop the pronoun.
Here are some possibilities:
Shop vendors should include a variety of imported products because such a variety solidifies the bond between countries and offers a wide range of choice to customers.
Shop vendors should include a variety of imported products because doing so solidifies the bond between countries and offers a wide range of choice to customers.
Note that there is also a third variation of this sentence, one in which the use of it would have been not just ambiguous but inappropriate:
- Shop vendors should include a variety of imported products because these products solidify the bond between countries and offer a wide range of choice to customers.