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Both sides are formally Roman Catholics. For centuries, East Timor was a Portugese colony, and the population is overwhelmingly Catholic.

I say "formally", because the Portugese did not strictly enforce orthodoxy, and allowed pagan and animist beliefs to continue, and they are still evident in rural areas.

There was always a very small Muslim population in East Timor, who were descendants of Arab traders. There was also a small Chinese Buddhist community. They were treated fairly during the colonial era.

The current Prime Minister of East Timor is a Muslim of Arab ethnicity, and he has challenged the Church's power over education in territory. But that, it seems, is not the cause of the current violence. All the other Govt ministers are Catholics.
During the Indonesian era, a small number of Timorese converted to Islam. Since independence, a small number have also converted to Protestant evangelical groups who have been active.

However, generally speaking, Timorese means Catholic. The Portugese were loved - everyone else seems not to be able to get on there. The Japanese occupied the island during WW2 and found it hot to hold. Australia is sailing into stormy waters with this involvement.