By out of parallel by 1/16" you mean the gap between the left and right outermost spirals varies by 1/16" around the circumference of the reel, right?
That’s 1.5 mm. That sounds like a fair bit.
I have four 35 mm reels and two 120 reels (one of the latter is “Pro Co”), some bought new and others secondhand. Except for one 35 mm reel, their gaps vary by 0.2–0.3 mm around their circumferences. One of the 35 mm Hewes reels, that I bought new a couple of years ago and know was never dropped, varies by more than the others: about 0.5 mm. Gaps measured by Vernier calliper with light pressure so as to negligibly distort the gap.
That said, the gaps between my two 120 reels differ by about 1 mm. One is about 57 mm and the other about 58 mm. Similarly, the gaps in the four 35 mm reels span a range of about 0.7 mm.
I haven’t found any real difference in ease of loading across these reels. They’re all easy. One of my used 35 mm reels has a dent (that I ignored in the above measurements because I measured at the four (eight) radial support wires, and the dent is right in the middle of two of these supports). Even that one is easy to load.
All the same, I might return a new reel with a 1.5 mm wobble if I had that option. But I’m curious to know if it loads okay.