“Public schools” means “government schools.” And where government goes, politics follows. If your children attend these schools, doubt not: They will be subjected to political indoctrination from the day they walk into kindergarten (or, these days, pre-K) to the moment they’re handed their diploma.
The tone of that indoctrination may change with the political landscape to better reflect the views of the party in power, but its substance will not.
“Public” schools serve two purposes which have long since grown to overshadow the one they’re sold on (teaching kids to read, write and do arithmetic).
The first of those purposes is to produce citizens who support, at least in its broad outlines, the existing political system. From elementary level social studies through high school history and civics, it’s all Pangloss all the time. The aim is to condition students to regard the existing system as a) inevitable and b) superior to all conceivable alternatives, and to prime them for participation in that system rather than for dissent from it.
The second purpose of the public schools is to produce workers whose skills fit the labor requirements of the political class, both the actual governmental elite and its privileged partners in crime.
Steve Newton's take on the issue is well worth reading too. It may look like we disagree, but it's more a matter of him being right as far as he goes ... and of me going quite a bit farther.