Keep them tasteful, but post!
Like
@billc says, we shouldn't be ashamed of what we do. And if you are, maybe another sport you can be proud of should be chosen.
The antis don't want us to post not just because they are offended, but more importantly because they want to further separate us from non hunters. What better way to do that than to limit our interactions with non hunters in any way they can?
I've always posted trophy pictures on FB and the vast majority of reactions to them has been positive. And they are a great starting point to educate thise non hunters who simply don't know the facts. This to me has far outweighed anything negative.
Last fall I hunted elephant and had to think long and hard about whether to post a trophy picture. In the end I did it, with a description of benefit the community and the species got from my hunt. It was very well recieved, which honestly surprised me a little bit.
A couple of months later the antis found it (I had made it public on purpose). They came in with their normal hate and threats. I used this as a further teaching and educational opportunity for my friends. Many were shocked at how the antis acted and said so. I blocked antis when they got out of line, but left most of their posts (I started deleting a few of the worst after the point had already been made).
I even debated one lady who of course tried to pass off emotion as fact and got a great opportunity to once again educate friends as to the anti ignorance. It was amusing actually as it was pretty obvious she wasn't used to arguing with someone who knew her information better than she did, and could untwist her statements.
Our society is becoming more and more urban. We are separated from our food sources, all of us to some degree. How many people here remember their mother going into the yard to kill a chicken for Sunday dinner? I don't. But my mother remembers her mother doing it. Point being, we've got to keep this gap from widening even further, which is what the antis want!
There will always be the few tasteless pictures that will be ammunition for the antis to use. And the morons that post them will always continue to do so. Does anyone really want THOSE pictures to be the only hunting pictures anyone on the internet sees???