Would have got rid of the original Lankan Tamils? There was a move to impose one language on the whole country and have reservation based policy in the govt/civil sector to help Sinhalese compared to situation inherited from British Raj, and fight Tamil autonomy/nationalist currents that spawned (modern nation state wise) in SL since the early 20th century...and yes a lot did get overblown on both sides....but I am unaware of any large popular intention/backing of "ridding" all the original Lankan Tamils (Jaffna, Batticalao and Trinicomalali)....esp on any religious basis.
It was largely political....that later did take some cultural and religious hues (as it almost inevitably would anywhere with the degree of the conflict) in various ways but it always remained rooted in a political conflict (and hence why the island is quite peaceful after the LTTE were defeated and bilingual state + various local autonomy got enshrined, i.e all factors that caused the conflict in the first place). Colombo had a majority Tamil population during height of the SL civil war....and many places of worship were both Buddhist/Hindu even during worst of the so called religious/cultural oriented violence (which had a extremist Church angle to it on the LTTE side). Maybe
@Gibbs @HeinzG can add/correct to this if they want.
It is very different to Rohingya crisis in that matter. I simply do not see much fundamentally connecting and integrating the Rohingya and Local Rakhine Burmese other than by peculiar traverse of history they are living in the same spot of land. Thus a perceived partition legacy more easily arises.