One way to define a counterculture is to say that it is a movement that goes against the values of the mainstream society. Using this definition, I would say that the religious homeschool movement is one that could be seen as a counterculture.
People who homeschool their children for religious reasons are generally doing so because of what they see as the secular and immoral values of our society as a whole. They do not want their kids exposed to the secular ways and to (for example) the sexualized clothing and behaviors that can be found in many public schools. They want a more traditional and Christian setting for their kids.
Because they are trying to buck the social trends, I would describe this movement as a counterculture.