In this arrangement of O God, our help in ages past I have found what looks like a breaking of the rule of harmony. In bar 1 we have I/3-vi. The tenor leaps up to C and the Soprano does the same. Isn't that a breaking of the rules of four-part harmony? It sounds like the tenor actually should have walked up to A instead of C. How should the voices in I/3 have moved to the next chord and what chord should that have been?
Well, this is a piano reduction where the voicing is absent. My guess is that the tenor is supposed to leap to E (well in the tenor realm) while the alto sticks with its previous tenacity at C. In which case this would be a voice inversion in singing and not a strict violation of "no octave parallels, please". Check the vocal score for comparison. Of course, if your interpretation is right also for the vocal score, that is a pretty bland case of octave parallels.
[Edit] After looking for the score online, I've seen a version where the chord before the leap does not have the G in the tenor (which presumably shares the E with the bass). There are other places in the score with just 3 different notes in the voices, so this seems like a simpler explanation. However, the version I found is also without lyrics, so it may also be the case that it is a different piano reduction where the arranger ripped out the octave parallel.
So finding a vocal variant still seems like the smartest idea.
How should the voices in I/3 have moved to the next chord and what chord should that have been?
I think this is a more pleasant solution:
[PDF] O God, Our Help in Ages Past - Hymnary.org
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