Rabbi Yaakov Bender said in a shmuz once that a Jew should learn from kashrus. In kashrus, there are two signs for an animal to be kosher – the hooves are external, and chewing the cud is internal. An animal needs both. One without the other is nothing.
He said that a Jew needs to appear as a Jew externally, but that’s not enough. You need to live your life correctly also, internally, where others don’t see what’s going on. He said straight out, many people wear hats and jackets and it’s like a pig – it sticks out its feet to show the hooves. I remember listening to the recording of R’ Bender – he yelled, “LOOK AT ME! I’M KOSHER! DON’T YOU SEE MY BLACK HAT, WHITE SHIRT, AND JACKET? I’M KOSHER!.” But, he continued, it’s no better than a pig – they show the outside, but internally, they’re not good Jews.
The outside doesn’t need to be a hat and jacket. It’s anything to show that we are Jewish, and shows it in a good light. R’ Gifter used to make sure his students wore nice clothing, with their shirts tucked in properly. Wearing a beat-up black hat and a stained jacket is not the outside part a Jew should be showing. It’s better to go without a hat than to wear one that is beat-up.
Unfortunately, there are stories coming out all the time about people who wear their hats and jackets, but don’t have the internal kashrus a Jew needs. Yes, people associate the hat with hypocrisy at times. Let’s hope that this changes, and that everyone has both the internal and external kashrus!