How can I help my kids adjust to our new neighbors' different values?
Your strategy here really depends on the age of your children. If your children are in early elementary school or younger, you may want to set limits on the frequency and location of their contact with the neighbors. You could, for example, allow your children to play with neighborhood kids when you are there to supervise and overhear what is said. In this case, you can tell other children the rules of your own home, but still allow your children to get to know their neighbors.
With older elementary and middle school children, I would try to have an open dialog with my children about time spent with these children or their families, so you can help them with values issues. I still would limit (but perhaps not completely disallow) time spent around these other children and families. It is important to tell your children what concerns you about the neighbors' behaviors or values. This should be done in a low-key but straightforward and honest way. Have a discussion with your children about the behaviors (such as profanity by the adults or children) that concern you, inviting your children's opinions and sharing your own.
Finally, it helps to connect with other children and families who share your values. These could be cousins, children who are part of your religious community, children you know through athletics or local children's chorus or theater.