If you're making the payments to the trustee as per the court's order, then there's no problem. You are far better off from a security/reliability standpoint than someone who has insurmountable debt or is in default.
Bankruptcy does not always mean that someone was financially irresponsible. Through the course of life, people acquire debt for many reasons; mortgage, car loan, furniture, medical bills... etc. If you lose your job, or are confronted with a huge expense - such as a serious illness - debts that you were paying off can become impossible to bear. That's why there are bankruptcy courts.
Sure, a lot of people spend too much with plastic because it's just too damn easy. They get over their heads and have to resort to a chapter 13. Others are just irresponsible and don't care. Usually, you'll find that these people are "serial" filers. They abuse the bankruptcy laws.
Even these people are not a risk to security. They might not be able to manage money, but it doesn't mean that they are untrustworthy.
Someone who is driving a jag, with a stated income of $40k, or who has recently acquired property that they shouldn't be able to afford, is a problem. Someone who passes a lot of rubber checks is a problem. Someone with too much debt and DOESN'T file a bankruptcy is a potential problem. (they may be bought off or coerced into doing things to relieve the debt)
If you filed one chapter 13, and are paying as ordered, you need not worry much. Now, if they find out about the stockpile of bootleg DVD's, moonshine, and knockoff Tommy Hilfiger gear you've been peddling.... Just kidding!