I'm not religious myself (because I perceive it as utter nonsense) and think of the Doctor as an artificial lifeform that can be considered a person.
As RegFan wrote, a human being is a complex biological machine in it's own.
We have numerous automated processed within our body that keep us alive for one thing, and the brain is a rather complex central computer that regulates EVERTYHING in our bodies.
To say that WE aren't machines would be idiotic at best.
We simply have certain limitations.
Data and the Doctor do not have certain limitations because they are designed in a way that gives them the ability to live indefinitely (barring an accident that destroys the technology that keeps them going for example or something else).
They are both just as succeptible to 'death' as we understand it as they are.
Do they exceed humans in mental functions?
Of course they do.
Just like you have humans today that are exceedingly smart, intelligent and with eidetic memories, the Doc and Data by definition incorporate all of those aspects because humans themselves perceived those as something to strive for (we strive for 'perfection' and aspects that continuously improve ourselves).
But I also agree with Guy Gardner in the sense that both Data and the Doctor surpass humans and that they were written in a capacity to be 'brought down' to human level.
It's like forcefully taking a person that's unique, and make them behave like everyone else.
I never has a problem with the Doctor or Data being considered a person.
Heck if artificial intelligence emerges in real life, I'd treat it like a real person (in fact, I sometimes already do that to my laptop and computers in general ... I like technology and am open minded).
In my personal opinion though, I find attributing outdated and backwarded aspects such as a 'soul' to any living entity is an insult to ones intelligence.
I agree that there are numerous things we don't understand about life and universe in general, but succumbing to religious views for an explanation instead of saying 'I don't know' is just cowardice and a way of comforting oneself.
'Beliefs' ... lol, such a rediculous concept.