Western Europe is a bit out of my knowledge base, but regarding the United States - yes, there's always been controversy around public education.

Thomas Jefferson pushed for a government funded for schools to supplement the hodge-podge system of academies, colleges, private schools, tutors, and religious schools he saw in 1779. By 1787, the idea of school being connected to government had seeped into the collective consciousness to such a degree the Northwest Ordinance, which informed new states ' constitutions, encouraged schools. School, though, at this point was limited mostly to white boys, and sometimes girls.

There were a number of attempts to arrange for public funds for schools via taxes in the early 1800's that were unsuccessful. Men with resources typically voted and advocated against such bills because they didn't want their tax dollars to fund schools for other people's children (as theirs would go to private academies or have a tutor.) Men with fewer means would often vote and advocate against them out of a concern their children wouldn't get seats because families of means would send their children, crowding out poor children. (Compulsory education - meaning the state has to provide an education to every child - wasn't yet a cultural norm.)

In the mid-1800's, things began to shift. The idea of schools for all (which increasingly meant white boys and girls, and sometimes children of color in the Northeast) was increasingly appealing to citizens, especially as a way to support democracy. However, there was vocal push-back, including Thomas Jefferson who wanted schools to remain under local control and not a larger government body like a district or state. Another source of controversy was the nature of the curriculum. Those who pushed public schools were often Unitarians or Protestants, which concerned Baptists and Catholics.

With each iteration, there was a degree of controversy. It's difficult to say if the majority of citizens were in favor as it was only men expressing their approval through votes, but it would be reasonable to call the concept controversial. The degree of controversy would vary depending on the community.

Source: Neem, J. N. (2017). Democracy's Schools: The Rise of Public Education in America. JHU Press.