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After my oppression by the heavy arm of the State last year, I finally got around to going to a police station (with REAL police) to enquire about the legality of taking pictures of people in public. Despite the platitudes of "it depends", I did get some answers.
(Summary of linked post: I took a picture of 6 female teenagers sitting in a playground explicitly marked out as being for preschool children, and was threatened with having the police brought down on me. Despite my photo being as far from possible from an upskirt or a downblouse [while still having females in it], the airport police sided with the girls, and I was forced to delete the pictures in the end.)
The officer I spoke to said that if you took pictures of a woman, there were 2 offences they could charge you under: insulting the modesty of a woman, and intruding into the modesty of a woman. Unfortunately I could not find the latter offence in the Singapore Statutes OnLine.
So the relevant law is my 2nd-favourite section of the Penal Code (my favourite is even better):
"Section 509: Word or gesture intended to insult the modesty of a woman
Whoever, intending to insult the modesty of any woman, utters any word, makes any sound or gesture, or exhibits any object, intending that such word or sound shall be heard, or that such gesture or object shall be seen by such woman, or intrudes upon the privacy of such woman, shall be punished with imprisonment for a term which may extend to one year, or with fine, or with both."
Given that the modesty of a woman is an extremely broad term (and the privacy of a woman only, perhaps, slightly less so), you can see how it is very easy to use this law against men (while the law is gender-neutral in wording, in reality we know that it is very unlikely to be used against women, due to Female Privilege).
On the other hand, the officer continued, if you took pictures of a man, only intentional harassment would get you in trouble, and furthermore it would be a civil case, not a police case.
I brought up the example of STOMP, which had lots of pictures of people, and he said it was better to ask the subjects of photographs for permission. I said street photography was about spontaneity, but he didn't respond to that
So, as far as I can tell, essentially you can't take pictures of women in Singapore without being at risk of being harassed by the police but men are fair game (as long as you don't "harass" them, so one-off shots should be fine).
This sort of case would seem to be ridiculous and not worth the time of those who ensure that Singapore has Low Crime. However, from other sources I know that the police tend to take the side of whoever calls them first - of whoever makes the complaint. And they also tend to investigate all cases - even ridiculous-sounding ones. And of course there's the bias against the man whenever a woman accuses him of having done something sexual to her.
So in this case, if girls are upset that you have taken pictures of them and call the police, you may get your camera (or phone) confiscated as 'evidence', and you may not get it back for weeks or months while you are being 'investigated'.
In the end, you will probably get a 'stern warning' instead of the case being dropped. While this is not as bad as being prosecuted in court (a possibility that cannot be totally discounted), this will count against you in future cases of a similar nature, which is great news if another female tries to use the law against you with an allegation of a sexual crime, since "If you commit any offence in future, the same leniency may not be shown towards you", and your camera/phone may not even be returned to you in the end (since a 'stern warning' is taken to mean that you did something wrong, they just chose not to prosecute you - in comparison note the phrasing when they drop the case entirely) and then be ordered destroyed by the Courts.
What might await you if you, as a man, take a picture of women in Singapore in public
I note that even in the unlikely case of the case being dropped, at the very least a few hours of your time will have been wasted, your camera (or phone) might be confiscated as "evidence" and you will be traumatised at being oppressed by the heavy arm of the State.
All in all, this is entirely consistent with what we know about the law and sex crimes committed by men against women in Singapore, and with other police advice that I have heard (that it is better for the man to settle, because the cards are stacked against him). Essentially, the man is screwed.