Less to the left than you might think. There was a sizable former conservative German Democrat base that supported La Follette for not being too supportive of WWI. Those folks made up the bulk of the Wisconsin GOP from the 1950s onward.
You cannot underestimate the importance of World War I in Wisconsin politics in that era. For instance, in 1920 Woodrow Wilson was so toxic here that Democratic Presidential candidate James Cox managed to get 16% of the vote in Wisconsin. La Follette's success relied on keeping the folks who were staunchly anti-WWI in his fold even though they agreed with him on almost nothing else.
actually from what I know about wisconsin politics, everyone was a republican until the 1950s when many LaFollettites who were formerly republican, migrated into the democratic fold as a backlash against McCarthy (remember McCarthy beat LaFollette in the 1946 republican primary). This is why the state started electing democrats at that time (Proxmire, Nelson, Kastenmeier etc).