Yes, boycott, but...
It will, however, take a while for all of this to filter up the corporate chain and, I think, there's a way to make our voices heard even more quickly.
You see, my wife and I shop at Target a lot. We fill a cart with our groceries every other week. This week, though, I will fill that cart, go to the checkout counters and ask for a manager. Then I will point out that this is just the beginning of the business Lawrence's store is going to lose because of the company's corporate policies. Then I'll leave the cart with the manager and go buy my groceries elsewhere.
A few restocked carts (and the time it takes to think about the price of all those items going back on the shelves) later and that manager will be making some calls to corporate. I guarantee it.
Show Target what you were going to buy, but now won't. Don't just boycott. Buycott.