I don’t know if “permitting different cultures” is how I’d phrase/frame it.

There always existed different cultures in the region and the Ottomans knew that. So they didn’t outlaw any culture or religion, but applied a dhimmi status - something nationalistic identities today try to misconceptualize - which actually translates to ‘protected persons’ who paid taxes to benefit from the Ottoman Muslim state protection and governance (not to be confused with full equality though). If you were happy to be under the Ottoman empire and pay tax, then you’re a part of it.

The primary influencers from Europe were Britain and France (they carved up the ottoman empire post WW1). They definitely had a hand in applying ‘soft power’ through minority groups such as those wanting more autonomy or who were disenfranchised by the Ottoman empire’s sub-par reforms and modernization (like pug mentioned).

But it wasn’t really one thing/person/imperial’s fault.

The Ottomans often benefited from limiting the development of competing political identities because maintaining imperial cohesion was important to the survival of a multi-ethnic empire. At the same time, there were competing factions within the Ottoman political establishment, each with different ideas about how the empire should be preserved and governed. So there were proponents who wanted to oppress, and others who didn’t.

The Europeans benefitted by carving it up because that was their colonial model (tried and proven in Africa and Asia). Whatever influence they exerted was generally part of the normal great-power competition of the era rather than direct control, and not necessarily of a kind that forced the Ottomans to respond with repression.