Democrat control of Chicago has been possible because they control the Irish vote, the Italian vote and the Polish vote.
Certainly enough Protestants vote Democrat to give the machine big victories but I would guess that they do make up the majority of the opposition. You could probably say for sure.
Chicago was about 65% Democrat in Kennedy's day, today it's over 80% Democrat (I think Gore got 81% of the Chicago vote when he ran against Bush in 2000, and won 49 out of 50 wards. Obama won all 50 but he's "from" Chicago so his numbers weren't typical) The non-Hispanic white population is now less than 32% of Chicagoans, so the Irish/Italian/Polish don't "control" much anymore except for elections in heavily white communities (it really helps to have an Irish last name if you're running for judge in Crook County, and a Polish last name if you're running for a legislative office in a white majority district). The south side is heavily black and protestant (usually Baptist), and overwhelmingly Democrat... they routinely get over 90% of the vote in most of those wards, far more than in the Irish-Catholic wards, where Republicans still get 20-30% of the vote typically. Then there's the hispanic wards, they're pretty heavily Catholic and also strongly Democrat, moreso than the non-hispanic white Catholic wards, but not as much as the black wards. The white protestants in Chicago don't have large enough numbers where anyone has really studied their demographics, though they tend to be from very liberal denominations (United Methodist Church, ELCA, there's a heavy Unitarian presence in the 19th ward although I wouldn't count them as "Christian", let alone protestant) Probably the non-religious secular whites have a bigger influence in Chicago than white protestants, and they also uniformly vote Democrat
I imagine the situation is similar in New York, St. Louis, Nashville (which has very few Catholics), Atlanta, Seattle, Boston (which is extremely Catholic), Philadelphia, San Francisco, Detroit, etc. Basically the Democrats have turned EVERY demographic in those cities in loyal Democrat voters. It's not like they just took over the Catholic communities but non-Catholics in urban cities are voting GOP. If that was the case, the Dems wouldn't be able to swing states like Illinois and Pennsyvania into the Dem column by winning HUGE in the cities.
And since Catholics in the suburbs and rural areas are NOT wedded to the Democratic Party (though sadly the suburbs in Chicago, Pennsyvania, Ohio, etc.), the overall "Catholic vote" nationally is now 50% Republican. Quite different from the "Jewish vote" where they typically vote overwhelmingly Democrat no matter where they're living. The division there is Orthodox Jew vs. all the other types of Jews, rather than urban vs. rural.