Were Judeo-Christian religious references part of the "Akira" movie's original dialogue?
These were not direct references to Christianity in the original.
When Akira is seen surviving the tank shot, the dialog among the onlookers is:

アキラ様
Lord Akira!
アキラ様の降臨だ
It's Lord Akira's advent/coming!
違う　騙されてないかん　あれはアキラ様ではない
No! Do not be deceived! That is not Lord Akira!
うるせー　アキラ様、万歳
Shut up! Long live Lord Akira!

With the use of 降臨 (kourin, lit. advent), it does sound somewhat... spiritual. But it does not seem to be a direct reference to Christianity at all, rather just the coming of a godlike being—Akira.
The second scenario is mostly the same, in that the subtext is spiritual but not Christian or even really religious.

おお、清浄の炎よ
O, flames of purity!
汚濁の街を焼き払い
Burn down this corrupt city!
我らの穢れた心を焼き尽くすがよい
Burn up our impure hearts!
恐れてはならぬ
Do not be afraid!
その身を炎で清めるのだ
Your bodies will be cleansed by the flames!

There's nothing about being believers or belief, and nothing about being born again.