The Southern Poverty Law Center describes itself as "dedicated to fighting hate and bigotry and to seeking justice", and is always expanding its notion of "hate". It has a history of spying on groups for leftist political purposes, and of acting as secret informants to the FBI. It has even incited violence against pro-family groups. Now it has issued a report arguing that opposition to Common Core is some sort of hate-driven far-right conspiracy.
The report says that Eagle Forum calls it "ObamaCore" and that a member "links Common Core to Nazism". Nazi name-calling is an SPLC specialty. According to Google, the SPLC web site has 5,260 web pages calling people Nazis. I don't think that any right-wing groups will catch up the the SPLC in Nazi name-calling.
The SPLC acknowledges that there are some valid leftist concerns about Common Core, such as it being developed in secret, controlled by an undemocratic elite, using inferior methods, having insufficient leftist influence, and being unworkable. But if similar concerns come from "Christian Right culture warriors", "Tea Party factions", "radical anti-government activists", and "powerful right-wing think-tanks", then the SPLC starts its name-calling and its reporting to the FBI.