No, but in muslim nations no other religions are allowed. I think that's more a political thing than religious. Any cultural change threatens the leadership in power. Especially in places were the leadership gets a lot of support from religious groups.
If the US government was supported to the same degree by say the Mormon church, then I think the same types of rules would apply, except that the Sharia would be Mormon instead of Muslim. You couldn't build a mosque in a fundementalist Mormon state, Utah actually requires beer etc. have less alcohol than the normal beer because Mormonism doesn't look kindly on drinking.
The reason that Islam gets a bad rap is the lack of political freedom in Muslim nations.