While most of the above is undoubtedly true, it is mainly about tuning guitars per se, and how to reduce or eliminate the effect of the capo on tuning. But the crux of the matter is whether you should ever tune a guitar with a capo on.
A friend of mine is an opinionated guitar snob (despite not being a great player), and he regularly spouts two misinformed beliefs:
(1) A good guitarist doesn't need a capo, and
(2) You, who by rule (1) is NOT a good guitarist, should never tune your guitar with a capo on.
In answer to (1), a capo has generally got very little to do with the guitar. It is about playing with other instruments, in most cases the voice. To play the same relative notes in a different key is not usually about making it easier, it's about making it POSSIBLE.
In answer to (2), you have to ask yourself what the aim is here; and my answer is that you want the guitar to be in tune with itself WHEN YOU PLAY IT! Let's not lose sight of that. So, having tuned you guitar to perfection, you put the capo on, hopefully in accordance with all the good advice above, and the guitar ends up out of tune. If you wish it sound OK, you must now retune it with the capo on. It's not rocket science.
The final, and by far the most important piece of evidence, you can get from Youtube. Watch live solo videos of Paul Simon, James Taylor, Bob Dylan, Joni Mitchell, Gordon Lightfoot, etc, etc, and you see them all tuning their guitars with the capo on, and then playing in tune. Maybe you don't think they are good guitarists?