I'm into old frames and this was one tool I wanted to add to my bag and just never got around. Well I did, and the first frame I attached to shows the hanger to be about 1/4" off at the rim.

How much misalignment is too much? If math serves me right on a 700c tire that's a 0.5868 of a degree off.

A. If the 1/4" off is in the vertical I would try to get it better.
B. If the shifting under load is working, then it's good.

I shoot for less than 1/8" in all directions.

You bought and paid for the tool, so might as well use it up to it's limits and your skill level.

Once I bother fitting the tool I generally get the hanger within a few mm TIR in all directions. However, I only bother when building up new frames, or when solving poor shifting issues.

Yeah, the "might as well" is a compelling argument but I figure I ask for a sanity check on how significant it is. Also part of getting my skills up.

Just as I love old frames I also love old components so I'm after the certainty of knowing who to blame (hanger or derailleur) if things don't shift right

Keep in mind that unless you have a good one (eg: Abbey tool HAG), there is going to be some slop.

Also, pick one spot on the rim to measure (perhaps where the valve stem is) so you aren't conflating wheel trueness with hanger alignment.

When making changes to the drivetrain of my gravel bike, I could not get it to index properly. I tried different derailleurs, different cassettes, double-checked cog spacing, changed cables, etc. I just could not get it to index properly at both ends of the cassette, at the same time. It was extremely frustrating, and many bad words were spoken. I bought a high-quality derailleur hanger alignment tool (Park DAG-3), and - despite it looking pretty close to straight to my eyes - I found that the alignment was actually quite a bit off. Proper alignment made ALL the difference, and smooth accurate shifting was the result. I adjusted the alignment of all my bikes, and every one of them shifted better immediately. It's not a tool that I use often, but I have used it again to re-set the hanger on my MTB after it got bumped pretty good on a ride. Having the right tool available is worth it to me. YMMV.

I was having some issues in the highest gear on a 12-speed drivetrain. Shifted perfect everywhere else, but got ticking, like it was not getting quite all the way over (limit screw not the issue). Found the hanger about 1/4" out top to bottom. Correct that to less than 1/16" and problem resolved.

Point is that 1/4" was significant for me.

Or clean/grease/adjust the axle bearings, then True the Wheel, Before doing the Hanger align...

Very worthwhile tool.

It's simply the mm gap, no need to think about degrees. If you look at online stuff, there's a few mm leeway, Park says 3mm. I know from personal experience that the more speeds in back, the closer it has to be. With my 9 and 10 speed stuff, I eyeballed it and never had a hanger-related issue. With the AXS 12 speed stuff I have, it has to be within a couple of mm. I use an inexpensive tool I got on Ebay and it works perfectly to get within a few mm, and therefore perfect shifting.