Same here. When I ask my friends who are not musicians and casual music fans about this, they always respond that they want to hear something really close to the original.
I don't find this to be true. As long as the audience can recognize, sing along and dance to it, most won't know the difference between a song that has been slightly modified to fit the band. Extreme remakes may be well less accepted (changing a genre or major tempo change) unless you're making something fit your genre that wasn't originally done that way. Aside form high end shows, most people have no clue about the details of most songs they know. Unless they listen to your version back to back with the original, it will all sound the same to most people in the crowd, or at least close enough for them to enjoy it.