When determining whether moss will damage your roof you should start with looking at where the moss is growing. For example, is it growing inside or around guttering and downspouts? If it is then it may start to prevent water from being able to drain away properly. It is best to remove the moss is this case because, if left, it could cause water intrusion and structural issues.
You will also want to look at the materials the roof has been constructed with to determine if moss will damage it. If the roof has clay or stone shingles then moss would not be a problem, however, keep in mind that moss holds a lot of moisture and this could have negative effects on the structure of the roof.
So, what if you determine that it is best to remove the moss? You will want to carefully research the best way to clean your roof based on its construction and the materials used. If not, cleaning of the roof may do more damage than the moss itself. You may also want to consider having your roof inspected as this will help to determine the roof's condition and help you decide whether removing the moss is really necessary.