[larsga]

First of all, many types of beer were historically not boiled. Quite a few still aren't. The mash, however, pasteurizes the beer.

That, however, doesn't last forever. In the conditions of the 18th century or whatever, microorganisms will get into the beer after mashing/boiling, so the heat treatment only helps for a while. The fermentation really does protect the beer afterwards, but it's a combination of low pH, alcohol, low oxygen, little nutrients, CO2, etc. Hops also help against gram-positive bacteria.

[wqaatwt]

Hops weren’t that popular until the 1400-1500s (or not used at all in some places like England) though

[larsga]

You're broadly right, but they were popular for most of the period we're discussing.

In continental Europe they were popular from roughly ~1000 onwards (see Behre 1999), in England from roughly 1500 onwards. In African and South American farmhouse brewing they're still not used. So it's a pretty complicated picture.

As the comment made clear, hops are only one component of what makes beer safe, though. Storable, safe beer for travel is documented already in Ancient Egypt.