Overall, moss and lichen will NOT adversely affect the integrity of your slate roof but there is one caveat to that answer.
Moss growth primarily occurs on the southern slope of your roof but can certainly grow on other slopes, just not usually to the same degree as the southern slope. We do not believe moss has any negative effects on the integrity of your slate tiles but on a low slope it can impede the water flow which can lead to leaking.
A leaking roof can be fixed or avoided by professional moss removal. If leaking has already occurred, offending slate tiles need to be removed, cleaned/scraped, and reinstalled after proper preparation including new sarking under the battens. Moss removal can be accomplished through scraping, pressure cleaning, and/or chemicals but keep in mind that all methods are temporary since regrowth will eventually occur.
Provided your roof has steep enough pitches to prevent these natural growths from impeding water flow, removal is simply a matter of personal choice. Many people prefer the moss and lichen as “character building” qualities that money can’t buy and only time can add. Architects will often even specify mossy reclaimed slates, especially with an extension to match the existing slate roof and home.