There is value in disregarding others' opinions of your actions and to let those opinions determine your identity and life decisions. However, if you claim to be a Christian and your actions contradict the identity of Christ that you claim to represent, the perceptions of others are a high priority.
We are being watched, by people who believe what we do and by people who don't. To both groups, a contradiction in our proclaimed identity and actual actions/beliefs causes issues.
Regarding fellow believers, the passage in Luke explains that while we are fully aware of our internal thoughts and private actions, people who are observing may not know the whole story and assume the worst. Therefore, we cause them to stumble and doubt the value of following Jesus because His followers are inconsistent.
Regarding non-believers, the difference between endorsement and acceptance is key. Jesus was accepting of everyone and everything, but clearly did not endorse everything. If we decide to endorse questionable behavior or justify our way into decisions that may not be clearly defined, inconsistency happens here as well.
Within any decision, word, interaction, relationship, life stage change, and behavior: Consistent alignment of belief and action is key.
