Is it more common to read 門 as かど or もん?
e.g. how would we pronounce the 門 in 彼らは門が開くのを待っていた。
When the kanji character 門 is used as a noun in itself (meaning a gate), it is usually read as もん, although it was also read as かど in older time. As other people say, 門 in your example should be read as もん in the modern Japanese.
The most common example of 門 read as かど in the modern Japanese that I can think of is a proverb 笑う門には福来る (わらうかどにはふくきたる). This 門 is read as かど and means a house. The literal meaning of the proverb is “Happiness comes to a home where family is laughing.” Progressive Waei Chū Jiten suggests two translations of this proverb: the more literal one is “Fortune favors cheerful homes,” and the less literal one is “Laugh and grow fat.”
I think もん is Chinese reading and かど is Japanese reading .
You would found かど is usually used for the Classic Movies