IME: "giving a pass [to]" is synonymous with "making an exception [for]". Whereas "passing up" or "passing on" (or as you said "passing over") would be closest

IME: "giving a pass [to]" is synonymous with "making an exception [for]". Whereas "passing up" or "passing on" (or as you said "passing over") would be closest to "not taking" or "skipping". OP said they "give a pass to" two veggies and despise all others. So I read it as they were making an exception to their "no canned veggies" rule.