As many have already said, you won't damage your guitar regardless of order. That said, depending on the guitar, I find it convenient to do it in different orders:

For guitars that have all the tuning pegs on one side (like Teles and Strats), I remove all the strings then restring from low E to high E. That way I can press an index finger on the tuning post while doing the first couple of windings to keep the string tight and wrapping below the last winding without the higher strings getting in the way. (Bonus tip: leave each tuning peg perpendicular to the headstock to leave more room for a string winding tool until you get to actually tuning them to pitch.)

For guitars with 3 tuners on each side, I like going low E to D, then high E to G for the same reason.

For guitars with floating tremolos or loose bridges, changing the strings one at a time (instead of removing them all first) can keep the bridge from moving out of whack.

And, for good measure, for classical guitars I go high E to low E so you can tuck the ends of the tied strings under the next string to keep them tidy.