There are conservative and liberal versions of any religion. Christianity has evangelicals but also Quakers. Judaism has Reform and ultraorthodox. But we only hear about the extreme radicals and conservatives in Islam.

Liberalism as an ideology is typically secular, so no, there isn't "liberal Islam" anymore than there is "liberal Christianity."

There are, however, plenty of Muslim people that believe the role of government is protecting human rights, believe one of those rights is property, and think the best way of achieving this goal is a secular democracy.

Turkey under the Kemalists is an example of a primarily Muslim nation at least attempting to build a liberal democracy.

You might say it goes against fundamentalist Islam, but guess what also goes against fundamentalist Christianity and Judaism?

Gay imams are an example.