You'd really have to talk to the rescue first. Some of them are flexible with their rules and some aren't.
You'll find that some rescue volunteers will talk to you and want to know the reasons behind your decisions (all of which are entirely reasonable as laid out in this thread), and others will just stop right there and reject your application without inquiring further.
Not only does it vary by rescue, but frequently it will vary by volunteer. For the most part, rescue volunteers are extremely passionate about the welfare of dogs, but not all of them are equally educated about all issues surrounding their training and care. You may run into volunteers who have weird ideas about bitework or who feel VERY STRONGLY about un-neutered dogs and are unaware of (or don't care about) the reasons to delay neutering until later in the animal's life.
It happens. The best advice I can give is to strive for understanding, try to be respectful of people's reasons and positions even when you disagree (remember: a lot of rescue volunteers have seen some pretty extreme cases, and these can result in them having jaded opinions about people and/or making incorrect snap judgments based on bad stuff they've encountered in the past), and just move on politely if you aren't making headway in a discussion.
MOSTLY, in my experience, volunteers do try to get to the bottom of ambiguous issues and give good adopters the benefit of the doubt. But not always. So, again: it happens.
Shelters tend to be much, much less stringent in their screening and adoption procedures. This can be good and bad. The good side is that it's usually much easier to adopt from them; the bad side is that you typically get a lot less information about the individual dog ahead of time (which can be an issue sometimes) and less support down the road if you happen to need it. A good rescue, like a good breeder, should be there for you if you run into problems after getting your new dog.