There are two and a half parts to this answer.

First part: if you are in LEO (low Earth orbit) (The only EVAs outside LEO were part of the Apollo programme) then you're inside the Van Allen belt and the radiation environment is therefore significantly nicer. No humans have been higher than LEO since Apollo.

Secondly, if you're outside the Van Allen belt, such as on the Moon, then yes things are nastier. But you're not there for very long. In particular, the annual radiation dosage on the Moon is somewhere between 100 & 400 mSv: on the surface of the Earth (well, in the US: it varies a lot) it's around 6mSv (this comes from this page) (see below on the units for radiation dosage). So the Moon is about 66 times worse than the Earth: a film on the Moon for a week gets about the same dose as it would on Earth if stored in the same conditions for a year and three months. Well, you can store film on Earth for that long, and in fact much longer, without significant ill effects, so a week or so is fine.

Additionally, most the film used was fairly slow, with ISOs (really ASA then) of 160 or below, & slow film is less sensitive to radiation damage. However on at least some missions (Apollo 8 anyway) some very fast film was used: see this NASA page:

On Apollo 8, three magazines were loaded with 70 mm wide, perforated Kodak Panatomic-X fine-grained, 80 ASA, b/w film, two with Kodak Ektachrome SO-168, one with Kodak Ektachrome SO-121, and one with super light-sensitive Kodak 2485, 16,000 ASA film.

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Radiation dose measurements are complicated, but the Sievert is a commonly-used measure; a rem is an older measure: 1Sv is 100rem, and a mSv is a milli-Sievert. None of these are necessarily very appropriate for film, since they all talk about the dose absorbed by humans. But they're the best I could find.