I think the most dangerous part of what you did (you already acknowledge most of it - being a little inflammatory etc.) is that even after this event you are still entirely intractable. You may have despised that car and have "preferred to delete the photo of it" than to say you were taking a photo of it (why ? That's what you were doing), but the "deletion of photo" method may not have appeased the neanderthals - by that stage the situation was already out of your hands. What would have been so wounding to your pride about telling the truth - that you were taking a photo of the car (whether you "despised it" or not is information they do not need to know) ? Seriously, forget the law and your rights - if you want to engage in a practice which many people view as intrusive, especially in an alcohol-fuelled environment, then it would behove you to be more accommodating and tractable. Sure, it's a free country, but there is no shortage of people spoiling for a fight and if you choose not to be tactful ANY time you are in public, don't be surprised at the result.
Just as an aside, you do realise you also put your friends in danger - not necessarily by taking the photo, but by refusing to tell the truth about why you did so, which would have likely minimized the situation. Karate this/karate that - real fights are VERY different (even without the potential use of guns and knives), but I suspect you had your friends' skills and sizes, and the number of them, in the back of your mind as a kind of "security blanket", which is very unfair on your friends. As to them using the word "fag", yes I absolutely see how this would have made you angry, but seriously - these people were clearly not the elite of society and I'm sure you hear stuff like this virtually every day. You need to know when to pick your battles and when to let things go - because if you always battle, you won't last long. Overall, if I am to be honest (which I am being), I think you handled this situation poorly. I'm sorry that you were hurt, but I hope you have learnt something from the experience (and saying you would rather delete the photo than tell these people you were just taking a photo of this interesting car suggests to me you haven't).