"What if they're wearing clown pants?" Firstly, people wear clown pants for many reasons. They're clowns, they like the roomy feel, they found them in a bin, etc. Secondly, if you're thinking metaphorically as in, "what if they're doing something so ridiculous that judging is warranted?" Maybe you need to think about why you don't have their freedom, to not follow social norms. Maybe they have reasons you don't understand.
The ultimate purpose of this verse, in context, is to counter-act hypocrisy. When you judge someone else, you ultimately reveal that you need judging. Jesus points our judgey eyes back at us and says "take the plank out of your own eye" first then help your brother.
In real life, I think this looks like mutual confession. If you find yourself judging your friend for some sin, do an inventory of your own heart and you may find that same sin. Instead of silently chiding them or faulting them behind their back, have a conversation with them. Ask them if they'll work with you, to pray to God and help remove the "plank" in your eye, and then help them remove the speck.
I spend a lot of my day in my own head. Solving problems at work, reading email, reading books, listening to podcasts and focusing on me. When I get home I talk to Kelly and watch TV but 75% of my day is in my head. I think a lot of people are just with themselves and in order to live with yourself you have to justify your faults. I have to find reasons why I do what I do otherwise there'll be a cognitive dissonance. This is how I can spend all day wearing clown pants, walk around outside and feel normal. My pants are justified. To me they are my life. What's wrong with my fashion choice? Then I notice someone else wearing a sweater vest and I think "Ha, look at that chump."
That attitude can become habit. "I am right and the rest of the world, if they're not like me, is wrong." I can become blind to my own foibles and make a fool of myself trying to rid others of theirs.
God help us with our pants.