Hi Dani,
I am an amateur artist too (impressionist) and when I read your post I thought about some of the reactions I received in the early years of my work. I trained with portraits, did sculpture and painted.
Some people saw my nude portraits as 'disgusting' just because they were nudes, some people saw my metal sculptures are 'disturbing' just because they were made of metal (incorporating metal bars and chains that helped to hold the work together). The works were not provocative, but provoked people because of their "own reactions" and own "internal issues", not because of the level of technique or the artist description that went with them. You know that Van Gogh's work was hated and received much criticism during his life, his works were designed to give people happiness by creating beauty. It took a long time for people to understand his style and appreciate his technique.
I understand how you are feeling, and wonder if you have had the opportunity to discuss the context in which the photo was taken? We all know you can take a photo, of a 'normal' situation, and depending on the angle it can look abnormal to some.
Have you spoken with the union about this issue and the subsequent treatment from your boss?
I would personally write an 'incident report' explaining what was happening at the time the photo was taken, and express how a 'slight of angle' can confuse a normal situation, and express your own dissatisfaction that the photo was posted without your consent, considering the reaction it has received. Express that you feel that the situation has become politically charged and your disappointment in the fact that simple communication, which you were denied, could have cleared the incident up.
Ask the union to participate, and ask that the 'incident report' you wrote be included in any 'file' pertaining to the incident and held with the union. Try not to be emotionally charged when writing the report and have a friend look over it to ensure that you are not letting your emotions in, just be factual and calm in your writing.
Good communication can solve just about any issue in my mind, and if your boss is a good manager (which I hope s/he is), then s/he will appreciate the situation was not deliberate and offer up an apology for lot allowing you to communicate your perspective and clear the air when concerns were raised. Your managers pride will be on the line for overreacting so don't wait around expecting an 'actual' apology. Sometimes people use a different language to apologize that also allows them to save face at the same time. Win, win in their mind.
The simple solution should have been to ask you about the context of the photo, then explain that some may not understand the context it was taken in, and ask that it be removed. But not all managers think the way I do.
Sometimes, managers (and people) say things because of their own issues. Try not to get paranoid about the silly comments managers make. I believe people sometimes say nasty things because they are scared - it can be described as another version of 'fight' response really. Write up your perspective and see what happens.
By all means look for a new job, but in the meantime, I believe you deserve to have the opportunity to communicate your perspective and your dissatisfaction with not being allowed to communicate your point of view (in a calm, non emotionally charged, non attacking way).