There are probably several reasons why some vets encourage people to have their dogs neutered - there is a big unwanted dog problem in this country, particularly in certain areas and obviously if dogs are spayed/castrated then they can't add to the already huge number of puppies born every year. From that point of view I can see why vets encourage owners to have their dogs neutered as not all owners are responsible - a lot of people still have the 'I want to let my lovely dog have puppies/be a dad because they're so special' mentality and still others don't see their dog getting out of their garden on a regular basis to go roaming as a problem. From a health point of view a castrated dog can't develop testicular cancer and it also lessens the chance of them developing infections such as balanitis (although the health benefits are not really clear cut, some studies have shown that castration may increase the incidence of other conditions). Of course some vets may do it just because that's what they've been taught to do without really thinking about the whys and wherefores and yet others may do it because of the money aspect, that being the world we live in and all.
For me it's a decision that should be made on a case by case basis and there is no blanket right or wrong view on it; it's right for some dogs and some owners and not for others. I think there are much more compelling reasons to routinely spay bitches than to routinely castrate dogs which is why Rodaidh is still intact at 2 and a half years old and will stay as such for the foreseeable future. I had Alfie castrated at just under 2 years old because he suffered from chronic balanitis (nasty penile infections) and it was the only way to really cure it. If that hadn't happened though he would probably have stayed entire for the time being as there were no behavioural reasons to have him done.
As for rescues, for the ones who have the 'existing dogs neutered' rule (not all do) I do understand where they are coming from as they are the ones who pick up the pieces of all the unwanted dogs and irresponsible owners day in day out and I have read some rescues saying that they have had experience of a lot of dogs 'bouncing back' into rescue if homed with entire dogs due to fighting, spayed bitches being mithered by entire dogs etc. (this isn't my opinion, just what I've read on a big rescue site when similar questions have come up). It's up to each rescue to decide on their own rehoming criteria. There are rescues who don't have blanket policies though, it's just a matter of finding one which suits you - Alfie was entire when I adopted Tilly and the rescue were fine with it.