The Irish to some extent, but moreover, Connecticut's never had the same "Yankee conservatism" culture that the rest of New England had up through the end of the 1980's (when it died in VT/NH/ME).
More along the lines of this.
Granted, there was some deep religious conservatism in the founding of the Connecticut Colony, but at the same time it also had some of the same Dutch influence that New York City and northern New Jersey had that tempered the devoutness of WASP Protestantism. I should note that the colony of New Amsterdam had strong emphasis on ideas like religious freedoms and civil liberties, inevitably leading to a more religiously tolerant native population than New England. Ideas like protectionism, military drafts, or martial law rubbed people in this cultural area as wrong and made them natural allies with the immigrant Irish and Germans who were immigrating to the area around the mid 19th century. Martin Van Buren, who spoke Dutch as a first language, was instrumental in pretty much forming the northern wing of the Democratic Party that was notably pro-civil liberty, pro-free trade, divided on slavery ("barn burners" and the like), for expanding American influence on the continent but against foreign entanglements (pretty much a continuation of the Monroe Doctrine), and generally in support of increased immigration and universal suffrage for all white males regardless of religion, class, or creed.
So basically, voters who would've trended Democratic due to the anti-authoritarian tenets of the party, making them odd bedfellows with the South.
That is my paragraph long answer, I can make a more detailed multipage essay long one for those who are into tl;dr posts.
