Which is better: to boycott young people who are not expected to do good, who curse religion and abandon prayer, or to mix with them and educate them, knowing that boycotting might mean boycotting a large percentage of people?

The best approach is to combine advising those who do not respond to your guidance with reducing your interaction with them. A Muslim is commanded to invite people to the religion of Allah, and "for Allah to guide one man through you is better for you than red camels." However, if you know that they are completely averse, then boycotting them is safer for your religion, for abandoning prayer, cursing the religion, and cursing Allah are among the gravest forms of disbelief.