Recently, I was on vacation in Asia, and was walking through a district on a Saturday afternoon. I noticed that there was a synagogue in the area, which appeared to have some architectural features that I was interested in taking a look at, so I went to the area to just look at the exterior of the synagogue and perhaps take some pictures for myself. I had absolutely no plans to go inside: for one thing, I'm not Jewish and I didn't know if it would be open anyway, and for another, I had a feeling that as a woman, I might not be appropriately dressed, since I was wearing a low collar and trousers and the place was described as MO on Wikipedia. In any case, I ended up being told by a security guard that I wasn't supposed to take pictures.
Since the impression the guard (erroneously) gave me was that photography was outright forbidden (perhaps for privacy or security reasons), I was wondering if I wasn't aware of something and decided that I would email the place for a clarification (in case I go there again). I ended up on their website, and noticed that they prohibit photography and mobile phones on Shabbat (which I understand the motivations for, and which explains what happened).
Is this a common restriction (for both Jews and Gentiles) that I should be aware of for synagogues in general?