I have here stated my final and my initial answers.
My final (and potentially "rude") answer - This is an answer that could be it's opposite:
Belief /Religion/faith (or lack thereof)?
Once I met a friend
A relation or connection is established between the individual and the religion/belief. Religion is a friend to many "in need".
Of a quiet bent This is the potentially rude part
Somewhat delusional (in a scientific perspective) or troubled/poor/traumtized/of misfortune (statistics show that people that are 'worse off' tend to be more religious than people that are 'well off'. sorry for the current lack of source(s), but I want to submit my answer!). This could also simply be misinformation / Misunderstanding. Beliefs and understands are quiet until stated or preached.
I followed at his heel
Your belief is with you always.
Everywhere he went
Til we came upon a door
In the case of Religion/Belief, this would be enlightenment/education/scientific proof against said belief. In the case of LACK of belief, this could be "the door to the church" both physically and mentally/spiritually through -> achieving an altered state of mind.
And our ways did part
the result of a new state of mind: they no longer go together. (to suddenly have faith would mean he leaves his previous state of mind behind.
To me it was an ending
religious no more (end of any belief) / no longer without faith = The end of the previous state of mind.
He thought of it a start
The beginning of a life based on scientific proof / new understanding OR spiritual enlightenment / a new found faith.
Belief fits on its own, since belief needs not be religious.
Once I met a friend
they are close (physically)
Of a quiet bent
The shoe or foot bends slightly physically, and the movement is usually quiet
I followed at his heel - obvious
Everywhere he went - as above
Til we came upon a door - this is where it stops making sense, and also, it seems too literal.
this answer only makes sense in the case of
a footsteps that would be only heard or seen outside..
EDIT: Figured out how to hide the answers, moved first answer to the bottom, small edits to clarify and clean up layout.