I would love to find the name of this font or fonts that are very similar to it.

Popularity  Suggested by elzadra 
Erbar Condensed  Suggested by donshottype 

You won't match this because it's lettering, but I have a suggestion.

Thank you, Elzadra. I thought as much. :^) I've been obsessing over this for years. I think I may have to design a font myself based on this lettering.

The lettering was created in an era when thick and thin [stressed] sans were popular.
AFAIK there is no narrow font in this class that comes close to the Church sign.
You might be interested, however, in Erbar Light Condensed, which dates from 1928. This is NOT THE FONT, but has similar proportions, particularly for the oval letters _C_, _O_ and _S_ as well as letters such as _W_ and _M_. Although it is not a not a stressed sans, it could be tweeked to make a rough substitute and provides some insight as to how letters not included in the sign could look.