This DBT concept is often misunderstood. If in DBT you're advised to encounter a situation non-judgmentally, it doesn't mean that you need to accept other people's bad behaviour. It simply means not immediately reacting to or judging a thought or situation. It is related to the concept of radical acceptance (which is also a major concept in DBT).
Non-judgmentalness is a good skill to develop within mindfulness practice as it helps set aside some mental space to take a break from the emotional rollercoaster of everyday life. It also is a good skill to use outside of an intentional mindfulness practice. Approaching stressful or upsetting situations from a non-judgmental perspective helps lessen the impact of the event on your mood and makes it easier to proceed with a Wise Mind or to make good choices in the moment. Also judging others tends to make us feel like others are judging us, and it also may reinforce the habit of judging ourselves.
It can be hard to identify judgments. Judgments can be thoughts like "Being sad is bad, I am weak for feeling this way" or "I should not be jealous" or "Having to do dishes is awful". Generally words like "should", "good", "right", or "fair" signal that you may be being judgmental. You can try reframing judgmental thoughts when you have them. For example, you may instead tell yourself "being sad is a normal human emotion, it doesn't make people weak" or "I don't enjoy doing dishes, but I like to have clean dishes so I will do them anyways."
It's okay to experience judgmental thoughts. You do not need to go through life being non-judgmental 24/7 (and judgements can actually be useful in certain contexts). It's even okay to have judgmental thoughts when you're trying to practice non-judgmentalness. It happens to everyone, that's why this takes practice. When you notice a judgmental thought, you can try to reframe it, or simply note it and let it go. Try to resist the temptation to judge yourself for being judgmental. Just move on.