Two of my daughter's 8 year old class mates taught my daughter how to use the middle finger. My daughter is now obsessed and wont stop. We don't use this at home and find it offensive. However she uses it all the time. So we have taken play dates away, we have put her on time outs. But she just won't stop. Now her 7 year old sister is trying it on for size. Any suggestions.
Have you tried explaining to her what it means? Not in its entirety of course, but maybe something along the lines of: "Giving someone the middle finger is like telling them, in the meanest way possible, that you dislike them. This goes beyond 'not being polite' and, besides making the person you are giving the middle finger to feel very bad, it reflects poorly on you. It tells others that you are disrespectful of others and their feelings."
If explaining it like above doesn't work (or hasn't worked already), try asking how she would feel if someone did that to her.
You can then use her responses to help her put herself in the shoes of those she is using the middle finger towards.
I have found that, in general, children don't want to hurt others. They may think something is funny or not think through what they are doing, which ends up hurting people, but they (generally) try learn from those experiences so as not to hurt others again. Also, at the age of 8, children are still learning how to tell the difference between "right" and "wrong" behavior when it comes to social interactions/how it impacts others emotionally.
One of my favorite parenting authors, Ron Taffel, writes about the "family envelope." We, as parents, create an envelope for the child, large enough to move and grow, but small enough to be safe. Children learn where boundaries are by pushing against the envelope, and when they hit that edge and realize they can go no further, it makes them feel safe. As they age, we increase the size of the envelope.
Your daughters are pushing the edge of the envelope, and the behavior you describe is an age-appropriate attempt at doing so. That you have tried multiple methods for stopping the behavior suggests a need for consistency in your approach. Remember that most envelope-pushing behaviors are attempts to get attention, so your multiple attempts to explain to them why the behavior is wrong are actually rewarding their bad behavior. They KNOW it's wrong, they are just pushing your buttons. Timeouts (which rob the child of any attention) should be the most effective way to deal with the problem if used with consistency.
I personally learned to use timeouts the 1-2-3 Magic way, which suggests that when a child exhibits an inappropriate behavior, you calmly name the behavior and say "That's one" ("We don't use that gesture in this family. That's one." Try it with no eye contact.) If the behavior or another attention-getting behavior follows, you just say, "That's two." Third offense, "That's three. Timeout." The child must go to her room for X minutes (X being her approximate age). The trick is to not spend time explaining the behavior or to give the behavior any attention. You don't even explain to her that this 1-2-3 thing is something new we are doing - just do it, she will figure it out. After a very short time using this method, you will find most behaviors stop with "That's one."
Ron Taffel has recently written The Second Family, which explains how your children's peers groups create a second envelope when they become teenagers, which makes parenting even trickier.