I realize this was addressed to PredFan, but these are interesting questions.
In what situations do you advocate discrimination and segregation?
I can't think of any offhand. Prejudice and bigotry are generally pretty ugly business. The question is whether it makes sense to make them illegal. I don't think it does. Government shouldn't be in the business of dictating who we associate with or why.
Should religions be allowed to have arranged marriage for their children.
Well, marriage is a contract, and my understanding is that pretty much all contract law is based on the idea that both parties have agreed to its terms voluntarily. So, no. Or, I suppose parents can arrange all they like, but once the child has the legal right to marry, they have the legal right to tell their parents to take a walk, and to disregard whatever arrangements were made on their behalf.
Polygamists allowed to marry young brides.
Children denied medicine or vaccinations because it is against their parents religious beliefs?
The rights of children, and how they relate to the rights of legal adults, is an interesting topic, both in the context of libertarian thinking and in the broader political world. But I don't think it reveals much about libertarian ideology - assuming that's your purpose. What we find frustrating is that so much current government policy treats adults as children, as though we are all incompetent and require a guiding hand.