Is sex right on a first date? There's no question of right or wrong in these cases. That's a value judgment which reflects society's double standards on sex, particularly with regard to women. It also does not take into account the gender differences in approach to sex which often dictates the situation.
In simple bald terms, for most men, sex is a form of release, which may or may not lead to any kind of committed relationship. They really see women as the vehicle for that release and expect, or at least hope, that a woman is going to give in when the moment seems opportune. However, when they do get what they want, especially when a relationship is the furthest thing from their mind, many retreat to avoid making any kind of commitment, because the very act would have coloured their view of that person. Men want sex, yes, but they hope you resist. Once you give in, you're regarded as 'easy'.
On the other hand, for most women, having sex is is a prelude to something else, to the possibility of a long term relationship. Sexual overtures are also tied up with personal appeal and how a woman feels about herself. To be desired and wanted is very powerful, so few women can resist such seduction, especially when a man will try anything to get it. I personally would not have sex on a first date because I believe that, if that is all the man is interested in, he is simply responding to his need, not mine and any relationship is a two way process. Loving myself as I do, I am more interested in what's beyond the sex. I have the confidence, self belief and feeling of security to resist any advances, no matter how persuasive the man. However, not every woman feels that self-confidence or assurance and sometimes, simply to be wanted and in fear of rejection, a woman will do something sexual which she might not have planned, especially if she is not used to being affirmed on a regular basis or lack self-love.
A simple rule of thumb is, no matter how passionate one feels on the date, if that person is not interested in you beyond the sex, or seems too keen to have it, despite your reservations, nothing much is likely to come from that, once the sex is over. Anyone who really likes and respects you will wait until you feel comfortable. But if you do have sex on the date, resist the temptation to beat yourself up about it. We always do what we believe is right for us at that particular moment, regardless of the consequences. Our decisions have nothing to do with anyone else's approval or disapproval, and hindsight is just a tool for insecure people who live in regret.