What is current christian doctrine on Rouseau's "Noble Savage"
hypothesis, by which I mean can someone who does not worhsip God/Jesus
(either through ignorance of or rejection of the christian belief
system), but whose personal morality means that they do not commit
sins, ever enter heaven?

Or, put another way, which is more important in the eyes of christian
dogma: living a good life or kissing God's ass?

If different sects of Christianity have different takes on this
question, could you please provide a breakdown? I'm particulary
interested in the Catholic and Anglican positions on thias issue.

I'm not too good on Catholic dogma so I'm just posting this as a
comment, but this is a section of the Catechism:

Believing in Jesus Christ and in the One who sent him for our
salvation is necessary for obtaining that salvation. 'Since "without
faith it is impossible to please [God]" and to attain to the
fellowship of his sons, therefore without faith no one has ever
attained justification, nor will anyone obtain eternal life 'But he
who endures to the end.'"

http://www.vatican.va/archive/ccc_css/archive/catechism/p1s1c3a1.htm#161

It seems to be clear that, for Catholics at least, worshipping God is
the important thing.

This is the issue that has divided the church for centuries - whether
one is saved by faith or good works.

It is very clear from the Bible. The Grace of God is your ticket to
salvation and not your good works.

Ephesians 2:8-9 (NIV)
8 For it is by grace you have been saved, through faith--and this not
from yourselves, it is the gift of God-- 9 not by works, so that no
one can boast.

But since a true Christian has accepted Jesus Christ in his heart as
the saviour, good works would naturally flow from person's actions.

Ephesians 2:10 (NIV)
10 For we are God's workmanship, created in Christ Jesus to do good
works, which God prepared in advance for us to do.

The line given to me in the course of a hard-line Roman Catholic
education 1960-1972 was that if someone had _rejected_ "the faith"
after being made aware of its existence, they were definitely put onto
the down elevator to the hot place.  Those who through no fault of
their own remained ignorant of "the truth", but nevertheless lived a
good life weren't actually allowed into heaven, but were allowed to go
to a place called limbo, a neither-this-neither-that sort of eternal
no man's land.