I've come across several liberal, non-religious homeschoolers in my many years of homeschooling. I'd say offhand that, in my experience, secular homeschoolers are about 20% of the total these days. They homeschool for some of the same reasons I do: they want their kids to be able to read, write and do math, and they worry for their safety.
These homeschoolers really are under the radar as far as the MSM is concerned. The media like to pretend that all homeschoolers are fundamentalist Christians.
I am not a fundamentalist but homeschool. My son's teacher was trying to make me responsible for his in school behavior, and the only way I figured I could do that was to go there every day. Not real feasible so I homeschool. I use all computer based cirriculum. My son is enrolled in the florida virtual school online and my daughter does switched on schoolhouse. If I could get her into the local charter arts school I would do that but my son is too "hyper" to go to regular school. A lot of the people in the home school group I belong too are very politically liberal even though they are "christian" of one sort or another.