Not quite sure what the issue is; if you only see them at the school events, and at sports events, they aren't really friends; they're acquaintances you know you will run into at specific events. Friends would be people you already truly spend time with away from these specific events.
Other than changing your kids' schools, or telling the kids they have to join new sports teams (do you really need to do that?), you will still run into these people at those places. If there are other parents in the school/sports circles who seem OK, make it a point to talk to those people, or just focus on your kids or significant other and when the parents you dislike come over, speak to them enough to be civil but then have something to do. If you volunteer to help with a school event or sports team, you will always be able to say, "Sorry, I need to go get the water bottles now" or "There's my husband -- have to go, we're running the pizza sales tonight" or whatever. If you're already volunteering in such ways, use that to be BUSY when they want to talk to you. And if they invite you here or there after events, tell them: "Can't make it tonight." Because you can't -- you choose not to. You don't have to give reasons.
Please don't put your kids in the middle by explaining to them that you think "these adults are rude and immoral in private." Imagine telling a kid that. They'll be confused, wonder if the children in these families are also bad people (and you don't say the kids are a problem, just the parents), and may repeat what you say. Kids will want details and will defend their friends to their parents. Do you want to go there with your child?
The person who posted and mentioned the "you can't play with me because you're not Catholic" post from a few days back was right -- kids WILL repeat things their parents tell them, or that they think they hear their parents telling them, even if you say not to. It will create much more drama than you want. If you want to be cool and more distant toward these parents, you don't need the additional drama of having them come to you angrily saying, "Your child told mine they can't hang out/can't talk because you say our family's immoral!" That kind of blow-up will be all over the school and sports community gossip in about one second and you, not they, will be seen as rude by other families.
Unless you really want that conversation to happen, just find reasons for you not to invite the one child over. However, if the child herself is nice and a good friend to your child, I'd think again before cutting her off from your child completely. Unless her parents want to come hang out while the kids play together, why not let the kids be friendly? If the girl's family is as rude and immoral as you say, your family and your child's friendship may be anchors for this girl and may help her see a better lifestyle.