the president isn't very visible. Probably quite a few Germans who aren't politically interested couldn't tell you who holds the office. But nonetheless when there's big social disagreements, anything extremely divisive or a crisis the president usually will have something to say, to unify people somewhat. Ideally the president is sort of like the moral consciousness or representative of the country as a whole. Also it depends on the person. Gauck our last president who was a Lutheran Pastor was quite outspoken on moral questions or democratic issues and somewhat of a divisive figure, the current president is more of a former career politician and much less so.