LB- In your example above, I would agree with the moderator that it probably shouldn’t be so complicated to say “I’m so sorry, but I can’t take the picture for you.”. There may be many reasons why someone can’t take a picture, and I don’t think anyone will ask for an explanation.
When it comes to these types of issues, I think that people often think they are more complicated than they really are. One big issue that people often have is the “shaking hands with members of the opposite gender” issue. People always ask, “what do you do if someone of the opposite gender wants to shake hands with you? Won’t they be offended if you don’t?”
Personally, I have rarely found this to be a problem. I simply tell them that I can’t shake their hands for religious reasons and they are usually fine with that. The only time it is a problem is when I am with other religious family members who do shake hands with not-religious relatives who then may think that I am rude for not shaking hands with them. But I think if anyone is causing a chilul Hashem in that case, it is the ones who shake hands and make the ones who don’t look bad. If no one did, then no one think badly of it.