Why do people think chicago is a liberal city just because we always vote Democrat ?

It's usually too much of a generalization to say a city, and definitely a whole state, is all liberal or all conservative. The political system is flawed in that much of it is winner-take-all. So if 50.0001% consistently vote one way or the other, it is tempting to attribute those characteristics to all of the population based on that just bare majority results. Granted, there are some places with more of a lean than others, but the more diverse the location, the harder it is to generalize. You see that especially true about large states. The common popular narrative says that California is a liberal state and Texas is a conservative state. Yet there are some very conservative people in California and some very liberal people in Texas. Much depends on where in those places you land. Places in interior California, and parts of suburban San Diego, are quite conservative while the larger urban areas are quite liberal. In Texas, all the large urban areas are quite liberal--and becoming more so--while the smaller towns and rural areas are quite conservative. 

Rules about such things as strip clubs and sexually oriented businesses tend to be guided by local political culture and who's in charge. What you are seeing in Chicago is a micro-version of what you see in many states with people assuming all one thing or all the other. FYI: one urban demographer called Chicago: one part San Francisco (no doubt the glamour part); two parts Detroit (no doubt the Rust Belt part).   

Try wearing MAGA hat, then go walk around the city. 

What does the presence of strip clubs have to do with political allegiance?  Texas is very conservative, yet there are lots and lots of strip clubs in Texas.  The Republican Party is full of dirty old men with lots of money who like to throw said money at young mostly naked girls.

Chicago is a DEMOCRATIC PARTY city because 60+ years of corrupt Democratic Party mayors have built up an invincible machine that grants patronage jobs, welfare, and favors to residents who support them.

The Republican Party has failed to gain traction because they have no such organization - plus most of their candidates are socially conservatives who try to force their concept of morality down peoples' throats:  Despite the fact that the city has a large Roman Catholic presence, most Chicagoans (and suburbanites) pay no attention to the Vatican, and their schools and churches are poorly attended and they are closing.

maybe cause others told them that