Obvously the ability to use backing tracks depends a lot on the style of music you're playing and your venue. If you're playing bluegrass, (which is a VERY small group of fans), and you used backing tracks then your reputation would be shot in a matter of weeks.
If you told the listeners up front that you were using backing tracks then that would work in an extremely small setting. Let's say 6-8 listeners.
When people come out to hear bluegrass, folk or Americana they rightfully expect that all of the instruments and vocals they hear are live.
Bob, I think there is quite a large group of bluesgrass fans. Newgrass, where newer songs are played by blue grass musicians, is gaining fans around here. Check out Walk of the Earth:
https://www.youtube.com/watch?v=aMu03WxjFu8I agree that bluegrass, folk, and Americana should not use backing tracks but I would add all bands should not use them except for the single, duo, and trio musicians. As Eddie pointed out money is a big issue for bands. I would much rather hear a small group of musicians with backing tracks than Karaoke!