The question why is powerful. When we vehemently set ourselves up against a particular sin (or sins) we inadvertently set ourselves up against the person who has committed them, leaving them embarrassed or feeling condemned. It's ridiculously hard and elusive, but I think we can be offended for God without being offended by people.
Instead, ask why. Why did they do that? Why do they feel like they need to do this? Why do I feel this way towards this person? 'Why' is the beginning of understanding, which leads to compassion (and for the sinner, 'why' is also a part of conviction). It won't minimize the sin, its consequences, or its necessary treatment, but it will add to us a lens of understanding. See the people God has given you, and love them well.
"Love must be sincere. Hate what is evil; cling to what is good." - - Romans 12:9
"When he saw the crowds, he had compassion for them, because they were harassed and helpless, like sheep without a shepherd." - - Matthew 9:36