I don't think any traditional religion is fully compatible with liberalism. Liberalism demands a very strong separation of religion and politics, and ultimately the sacred and profane. I don't think this is compatible with any traditional faith, given it implies an unbridgeable duality of political and social life from religious and spiritual life. Islam may be more explicit, but I think for Christianity, Buddhism, or just about any traditional religion, all spheres of life have their ultimate pattern in the transcendent. This seems to have been generally assumed by Christian divines before the eighteenth or nineteenth centuries.

This doesn't mean the Muslim (or Christian, Buddhist, whatever) has to support intolerance and oppression. There are good traditional arguments why persecution is a bad idea, not least that it tends to warp the faith of persecutor, making it more worldly and a matter of worldly power than spirituality.