They do it in a round about way, such as by teaching that evolution eliminates the need for a Creator. The Bible teaches intelligent design.
I never took evolution to be an alternative to creation necessarily. The way I always understood evolution was the same way I understood mathematics, electron theory, etc. That is, it is man's way of explaining the world around us. It is not necessarily man's attempt to defy God. For example, we study our atmosphere and define theories about how it works. We theorize that water evaporates from the land and sea resulting in water vapor, which rises to the upper atmosphere where it cools and condenses to form clouds of water droplets. Eventually these water droplets congregate enough and grow large enough that gravity takes over and they fall to the earth as water. That is a scientific explanation of why it rains. But does it have to mean that because science is providing a human explanation that science is defying God? Not necessarily.
Consider the trinity. It is nearly impossible for man to discuss and/or explain what the trinity really is without a fight ensuing. Why is that? Because when we try to explain it we are trying to explain Godly things using human understanding.
Cultural relativism is also unofficially taught in some venues. That is, they teach that all belief systems are equally valid.
I don't recall ever hearing a teacher suggest or teach this. Yes, we looked at some "ancient" religious beliefs such as Greek mythology or Egyptian hieroglyphics or American Indian paintings but it was never taught to be either godly or ungodly. It was just brought up as a lesson in historical religious beliefs and nothing more.
If we as parents really cared so much about what our kids were taught, we would take an active role in their education and know what they are studying and thereby provide our kids with our own influence. But this is not the normal way we do things. We send our kids to school (what I refer to as daycare) and expect the school system to do it all. Even the school systems almost demand that we parents get involved but we parents are too lazy and busy with our own lives to do so. I can't remember how many times our school teachers and administration promoted parental involvement with our children's education. Go to a school board meeting and see how many parents attend. The answer to that question will speak volumes.
More subtly, teachers tend to try and teach their moral code to their students. That is, how students should treat each other in class, and outside class. If the teacher happens to be an unbeliever...
I'm not quite sure what moral code you're talking about that would not be taught by society in general. Examples of this is same sex relationships, sexuality outside of marriage, etc. Our children are exposed to these things far more relevantly on the street and on the other "teacher" (the television) than they are in school. In school they spend 45 minutes to an hour in class learning about mathematics, government, science, English, literature, history, among others. The school curriculum does not include teaching about morality. That is taught in the home but what are they learning in the home?
In the home they are learning about infidelity, selfishness, drunkenness, drug abuse, lack of commitment and broken marriages (about 50% end in divorce), and irresponsibility. In addition to half of our marriages ending in divorce, nearly half of the children born are illegitimate, meaning the parents weren't married at all. This doesn't leave very many children living in strong solid families does it? According to an article I found from the National Review dated October, 2012....
72.3 percent of non-Hispanic blacks are now born out-of-wedlock;
66.2 percent of American Indians/Alaska Natives;
53.3 percent of Hispanics;
29.1 percent of non-Hispanic whites;
17.2 percent of Asians/Pacific Islanders.
40.7 percent overall: a disaster.
Look around. What percentage of children do you suppose live in a two parent family that do not have step brothers or sisters they are or are not aware of? My guess is that percentage is extremely low and becoming a very rare commodity indeed.
Like we do with everything else in today's society I am of the opinion that we try very hard to pass the blame on to someone else rather than own up to our own responsibility. "It's not my fault" seems to be the catch phrase of our times. The government doesn't do enough. The government needs to take care of me. The government is teaching my children incorrectly. The government, the government, the government....
But what are we doing?