"If people searched your belongings after you died, would they be surprised at what they would find?"
"About morals, I know only that what is moral is what you feel good after and what is immoral is what you feel bad after."
-Ernest Hemingway
We naturally feel internal discomfort anytime we speak against our thoughts, or act against our words. This is a subconscious mechanism to have us always stay congruent.
I don't think anyone I know would describe me as a "moral" person. I'm almost completely indifferent to both politics and religion, I frequently debauch until sunrise, and sometimes I don't wash my hands after I use the bathroom. My sense of right and wrong is often directed by how I feel at a given moment. Good and bad are matters of perception. Morality is subjective.
My only concrete "moral" is congruence. Congruence is having all of your thoughts, speech, and action in alignment. Congruence is about representing every aspect of yourself, good, bad, and ugly without filtering.
If there is something you do that you would be embarrassed about, either stop doing it, or stop being embarrassed. To continue doing something incongruent with your image is a crime against self. If you truly believe that you are doing the right thing, then you should be able to defend your actions without shame. You are whoever you are. Act that way.