I agree with @dpworkin that it’s a GQ for the fundamental issues it raises… but “plastic bags” is a relatively trivial example. That is, you can be as environmentally conscious as you wish to be, but you aren’t the gatekeeper for plastic bags. And plastic bags in and of themselves are pretty much a non issue environmentally. Oh, improper disposal is a problem, and non-biodegradable bags will last a long, long time before they break down (although they will)—but not all plastic bags are created alike. Many these days are made from corn starch derivatives that break down quite soon in sunlight.
Aside from the issue of whether people should or should not have plastic bags, the consumer can more than likely appeal to another cashier, or to your boss, or just avail himself of the bags that are within easy reach of the cashier station anyway, and bag his purchase as he wishes. You’d be risking your job, alienating your boss and pissing off his customers (if not driving them away) all for no good reason. (Paper bags have environmental issues of their own, quite aside from the fact that they’re made from trees. Spend some time around a paper mill someday and you’ll understand that better.)
If you have the courage of your convictions, whatever they are, then I suggest you start a business along the lines your conscience dictates, and see how that goes.
As for the moral issue, I do agree with the right of a pharmacist, for example, or a surgeon, to refuse to support termination of a pregnancy if he feels that strongly about it. It would be interesting to ask that person, though, how he would feel about the possibility of his daughter having been raped, and whether he would require her to carry her baby to term, too.