Yes and No. By that I mean, the Klan took an interest in a number of political positions which were "normal", but for the most part they nevertheless brought with them their vision of a White, Anglo-Saxon, Protestant America.

So for instance you bring up education, and this was something the Klan certainly was interested in. In many municipalities where the Klan had political clout, Klan affiliated persons would be on the school board, if not the superintendent. If anything, control of the schools was considered one of the most important local issues, because it controlled what children learned. Now that doesn't mean the Klan was entirely overt in how it sought to exercise that influence, they weren't holding cross-burnings during recess, but this excerpt from an editorial printed in a Klan publication gives you an idea of what they saw in the matter:

Any intelligent Protestant knows when you educate a man to believe he can be saved without the living God, that he is not a true American citizen, for it is impossible to be true to this country and at the same time believe that his existence on earth and in eternity depends upon a foreign mortal. [...] Americans arouse yourselves; don’t be cowards, for God hates nothing worse than cowardice.

The Klan saw the schools as a way to mold good, patriotic citizens, to instill in them good Protestant values and keep them away from Popery. One of the most important issues for them was keeping the Bible in the classroom. The result was advocacy for increased funding of public schools. The flip side though was a direct attack on private schools, especially those run by the Catholic Church. In Washington State, a Klan backed referendum to do so lost although still managed to pull in over 100,000 votes, while in Oregon the Oregon Compulsory School Bill that was initiated by the Masons, but likewise supported by the Klan, passed the legislature, but was struck down by the Supreme Court as unconstitutional. Federally too they backed a string of bills in the early 1920s that sought to create a Department of Education to increase government control over educational institutions would have increased education spending, but were cause for great concern from Catholic and non-white groups. In the former, they saw it as an assault on their ability to run parochial schools and provide a Catholic education to their children, while in the latter, to quote a member of the NAACP Board, it would

perpetuate and reinforce the present educational discrimination in the South by appropriating federal money to be spent, without federal control, by state and local authorities.

Because, as you allude to, education was such a mainstream issue, Klan involvement in education reform was seen by its leadership as a way to in turn make the organization more politically mainstream, but their perspective on the issue just can't be separated. The fears of Catholic and African-American groups were quite on the money. Hoping to ban Catholic schools and require Bible readings in class, to quote the Grand Wizard Hiram Evans, the Klan aimed to "take every child in all America and put him in the public school of America.. .. [w]e will build a homogenous people, we will grind out Americans like meat out of a grinder." The Smith-Towner Bill, one of several the Klan backed, would have provided $100 million in funding for a new Department of Education, but as a poison pill for most non-white or non-Catholic groups that forced uniformity and "reform" in a way many wouldn't enjoy.

To use another example you bring up, the Klan was mostly anti-Union, the national leadership disapproving of strikes and labor agitation, which as you might suspect, they associated with foreign elements. Although this stance wasn't entirely consistent, the exceptions prove the rule. An Oregon strike by the Union Pacific Railroad included several hundred Klan members, a sizable minority of the 850 members, but in explaining their involvement, they portrayed the abusive supervisors as mostly Catholic, and heaped a great amount of opprobrium on the strikebreakers, which were mostly African-Americans, or Asian immigrants. The Klan also used the presence of non-white strikebreakers to try and recruit from the ranks of white, striking, non-Klan workers. Again though, this was mostly choices at the local level, not from the National leadership.

So while admittedly, in one sense I have clearly not answered your question, hopefully the underlying intention I'm seeking to paint is clear, namely that the approach to policy by the Klan can't really be separated from their commitment to "100 Percent Americanism". Racism and bigotry was the underlying core of their identity, and more importantly, the lens through which they viewed the world around them. So something like Education policy wasn't something they could understand as separate from their views on American identity, and if anything it was a core vehicle for them to advocate for it. Likewise other issues which might not immediately seem grounded in xenophobia similarly tie into such views. Klan support for Prohibition, for instance, tying into views about lower class immigrant communities such as the Irish and their propensity for drink.

It is hardly exclusive to the Klan, and frankly more of a general rule, but they certainly stand as excellent illustration that racists are, well, racist. Racism and bigotry is a worldview that can't really be separated from how a person or group will interact with the world and understand the issues of the day, or the people around them. What made the Klan such a political force was because they could insert themselves, to a degree, as a part of normal politics, with millions of members involved in all levels of politics, and bringing with them the Klan worldview.

Sources

Baker, Kelly J.. Gospel According to the Klan: The KKK's Appeal to Protestant America, 1915-1930. University Press of Kansas, 2017.

Dumenil, Lynn. ""The Insatiable Maw of Bureaucracy": Antistatism and Education Reform in the 1920s." The Journal of American History 77, no. 2 (1990):

Holsinger, M. Paul. "The Oregon School Bill Controversy, 1922-1925." Pacific Historical Review 37, no. 3 (1968): 327-41.

Laats, Adam. “Red Schoolhouse, Burning Cross: The Ku Klux Klan of the 1920s and Educational Reform.” History of Education Quarterly 52, no. 3 (2012): 323–50.

McVeigh, Rory. The Rise of the Ku Klux Klan: Right-wing Movements and National Politics. Uni. of Minnesota Press, 2009.

Pegram, Thomas R. . One Hundred Percent American: The Rebirth and Decline of the Ku Klux Klan in the 1920s. Ivan R. Dee, Sep 2011.

"The Fifteenth Conference" in The Crisis, Nov. 1923. 221-224