There is a difference in the commands given in Romans 12:20 and 2 Thessalonians 3:10 because there is a fundamental difference between the people addressed in each text.
In Romans 12:17-20, Paul tells Christians how to deal with their enemies. They are not to repay evil for evil (v 17). They are to live peaceably (v 18). They are not to take vengeance (v 19). They are to do good (v 20-21). So, if the Christian knows that his enemy is hungry, it is right to feed him. In doing so, he may influence his enemy for good, and draw him towards God.
In 2 Thessalonians 2, the context deals with unfaithful Christians (v 6). If a Christian chooses to be a busybody, and will not work to provide food for himself, Paul commands that others not meet his needs. To do so would be to condone his laziness. Rather, this person is to be noted and not received socially (v 14). But, as Paul gives the instruction, he emphasizes,
…do not count him as an enemy, but admonish him as a brother. (v 15)
One text deals with a non-Christian who presents himself as an enemy, the other is a Christian who is unfaithful.
There is no contradiction.