I disagree. I believe that if your children have absorbed the values they learned at Bais Yaakov (or wherever) and at home, their “purity” is not in danger because they should already have the tools to separate the wheat from the chaff when it comes to the secular world. I have a friend who went to Bais Yaakov and took courses at a community college before she was in shidduchim (and no, she did not have to borrow money in order to do this; she contributed her earnings from a computer repair job and her parents paid for the rest up front). One of the courses was in oceanography. She told me with a smile, “They believe that the world is billions of years old!” Today, she is happily married to a great guy and has a baby (actually, she missed my wedding because the baby was born four days beforehand, but her husband stopped by to wish us well) and because of those courses, she is more than adequately equipped to support her growing family. It’s not like she didn’t already know that the secular world believes such and such. So when she encountered it in college, she was able to just laugh it off, write whatever the professor wanted to hear in the exam book, and get her degree without any damage to her faith or observance. If there are children out there (of any hashkafa) who reach the age of 18 and are unprepared for college because hearing these things from non-Jews will shatter their emunah, I blame not the non-Jews but the parents and teachers, who clearly didn’t do their jobs properly.
Incidentally, I learned Greek mythology in high school English in an Orthodox day school. It’s called mythology for a reason– we read it for its literary value as a work of fiction, not because we chas ve’shalom attach any importance or sanctity to the named “gods”. I went on to graduate from a four-year college with a majority Jewish population and strong Orthodox presence. Yes, I have loans, but I know I will be able to pay them off, and I actually became more religiously observant in college, not less.