Medill Reports has this interesting article about Illinois primaries. The focus of the article is whether Democrats will choose a Republican primary ballot on March 20, with the motivation of voting for a Republican presidential candidate perceived to be a weaker general election opponent to President Obama. The article says that many Illinois voters don’t realize they are free to ask for any party’s primary ballot, regardless of which party’s primary ballot they had previously chosen.
This is actually standard practice in Illinois, though more so downstate. If you have a county which is solidly Republican, it’s routine for self-identifying Democrats to vote in the Republican primaries, as there are often hotly contested local races on the Republican side. Along similar lines, self-identifying independents will almost always gravitate to the most interesting primary ballot.
By extension, you can argue that one reason why so many people in Chicago claim to be Democrats is because they think they have to register as one thing or another, and they think that since the only races that matter in the city are Democratic primaries, they have to be Democrats or their votes don’t count.