I'm afraid I'm only familiar with the Hospitallers' state on Rhodes, and so my answer will only address that aspect of your question.

The attitude of the Knights of St John towards their Greek subjects on Rhodes was cautious. They could not anger the Rhodians too much as, as you point out, the Hospitallers were in a minority. There were probably no more than 300 military brethren (knights and sergeants) in the eastern Mediterrenean after 1306. At the fall of the island in 1522 only 290 of about 7500 defenders were knight-brethren. The Order desperately needed the Greeks to work their farms and to man their castles and ships. As such, the Hospital restricted the native population's rights only so much as necessary to enforce their control over the island.

When the Order occupied Rhodes in 1306 (a conquest not completed until 1310), they expelled the Greek populace from the centre of the city, pushing them into the outskirts. The Greeks did lose some property as the new Latin (Catholic European) settlers were soon trading lands and houses with each other, but no exact records survive to show the scale of the confiscations.

However, the Greek populace continued to play a role in the government of the town. In 1439 it was agreed that both Latin and Greek citydwellers had to pay taxes, they were entitled to be consulted on this and each side to was to be represented by a representative from their own community. The natives retained their own judges and courts and, from about 1350, the Order's slaves were usually non-Greek in origin. Also, the Greeks weren't restricted to living in any one area of the town either, though only Hospitaller brethren could live in the collachium, the the area directly around the castle.

Intermarrying was allowed between the Latin settlers and the Greeks. Sometime between 1319 and 1346, Richard Bovis, from Provence, arrived and worked as a servant on a farming estate called Vilanova. There he married Sophia, a local Greek serf. Though their children were baptised in the Roman Church. Children of such marriages were largely treated as Latins, except that they were required to perform military service like the Rhodians.

Military service was required of the Rhodian Greeks, a situation little different from any populace in Latin Christendom. In this case it was called servitudo marina, a hereditary requirement for these Greeks to serve on the Order's galleys. The Hospitallers also employed Syrians and Greek Cypriots as soldiers.

The Order's treatment of the Greek Church again shows this practice of enforcing control, but not heavily oppressing the Greeks. When the Hospital and the Greek Church arranged their surrender, the Grandmaster of the Hospitallers was given control of nominations and grants within the Greek Church on the island, whilst the Latin archbishop was given half of the Greek Church's lands. However, there was no programme of coercive conversions and Orthodox priests retained formal roles like notaries and informal positions as village leaders. The Greeks had to accept the papal supremacy, but were allowed to still worship in the Greek rite and to conduct services in Greek.

The Hospitallers also tolerated other groups on the island. An Armenian church was established on Kos in 1366 and by 1440 there was a Syrian church on Rhodes. There were also two Jewish quarters on the island.

On the whole, relations between the Hospital and the native population of Rhodes were quite peaceful. A Greek visitor to the island in 1342 stated that the Rhodians missed some of their old freedoms, but were glad of the economic prosperity that the Order brought and the defence they offered against the Turks. The Hospitallers did limit Greek power. To make themselves rulers of the island they had to confiscate land from the church, secure the castle and its grounds, and to demand military service from the natives. However there was no sense in angering the natives, people that the Order relied upon for manpower and labour.

Sources:

Anthony Luttrell, 'Settlement on Rhodes, 1306-66', in Peter W. Edbury (ed.), Crusade and Settlement (Cardiff, 1985), pp. 273-81.

Anthony Luttrell, 'The Island Order State on Rhodes', in Emanuel Buttigieg and Simon Phillips (eds), Islands and Military Orders, c.1291-c.1798 (Farnham, 2013), pp. 19-28.

Helen Nicholson, The Knights Hospitaller (Woodbridge, 2001).