Yes. Companies who you trust with your personal data should pull out all the stops to keep that data secure. If that store cannot guarantee some level of security, then they can no longer be trusted with that information. Until this store can get these things in order, it is the smart decision of the consumer to reduce further possible exposure.
I was very unhappy with the way that Target handled the situation. I will not use my card there again, and because the closest one is 30 minutes away have gone there less and less. I don't feel they moved quick enough or made a heart felt apology I felt like it was pushed under the rug.
For me personally, I have lost faith in Target as a corporation. This security breach was unacceptable on every level. A company the size of Target should never have been able to fall victim to such a breach. It inconvenienced me with having to get a new debit card number and change so much that it left a bad taste in my mouth.
For me personally, every time I go into a target I am reminded about their data breach. I tend to only go to target for things I need very badly and when it is the closest option. For any other purchases I tend to either drive to other stores or order them online.
I have not once in my whole life shopped at Target so it really doesn't change anything. I don't nessisarially shop with a credit card either so that also doesn't factor in how I shop anyways. I mainly shop at WalMart and Dillions. It is an inconvience though and I don't think this has made me want to shop there.