Paul addresses the issue of conflict in conscience in the early Roman churches. Just as Rome was a city overflowing with diversity of ethnicities, religions, and thought, so too within the the young church was the same cultural diversity. This resulted in clashing convictions of conscience. Because there was agreement over essential points of doctrine, Paul calls his audience to not engage in conflict over these grey areas of differences but instead, preserve relationships and conscience.
He tells them to accept the person but not necessarily agree with them, that we are accountable to God for our choices, so don't judge other's choices. Don't put obstacles in the way of a brother. Pursue peace by focusing on what people really need. And finally, be a person of conviction.