I also found this jarring at first. Faceless institutions and the wider systems in which they operate are set up as "acceptable targets" by Mickey's backstory. Most of Mickey's actions are seen, in his eyes at least, as redressing the balance between these systems and the poor hard-working souls that generate a profit for them (e.g. Mickey's father). Most of the losses suffered by victims of the short cons would be reclaimable on insurance, and any money taken in the ATM scam in "The Con is On" would be credited back to the account holders by the bank. Far from feeling bad about these, Mickey would probably score them up as a victory.
As for the claim that they aren't thieves, this is clearly contradicted (and lampshaded) by the bank raid in "Cops and Robbers". It is also made clear a number of times that the other members of the gang are less rigorous in the application of the group's moral code (e.g. during Mickey's absence in "Picture Perfect" the rest of the group bankrupts a small business and puts all of its employees out of work). So in-universe, there is not so much a plot hole as somewhat dishonest individuals being less than completely honest about the nature of their business.
However, the real reasons for the difference in moral treatment of short and long cons probably lie out-of-universe. For the long-con it is important the viewers root for the protagonists, and for this reason they must be made out as something more than money-grubbing criminals. The short cons seem to exist largely because they are cool, but also to remind the audience that the gang members are very good at what they do. When every long con hits a snag 3/4 through each episode, the audience might start to question the grifters' informed abilities - including a number of successful short cons counteracts this effect. However, with the pacing of these scenes the writers are unable to take time to explain how one loss might be reclaimable on insurance or how a certain mark was an acceptable target.