I expected repeating command blocks on "always active" to always run in the same order after a server restart.
What actually happens is that they sometimes change order when the chunks containing them are reloaded.
Steps to reproduce:
1.

/scoreboard objectives add Test dummy
/scoreboard objectives setdisplay sidebar Test

2. IMPORTANT. Go to spawn, and move yourself a few chunks towards positive X/Z. In this general area, the chunks farther from spawn should load after the ones closer to spawn (or, at least, they did when I tested this).
3. Place 3 repeating command blocks in a row, in the same X/Y coords, in order from negative Z to positive Z, making sure that at the third one is in a different chunk than the first two.
4. Add the commands:

/scoreboard players set @a Test 1
/scoreboard players set @a Test 2
/scoreboard players set @a Test 3

5. Mark the third command block (the one in the different chunk) as always active, then the second, then the first. The sidebar should display 1 for your name.
6. Close the server and re-open it. The sidebar should now display 3 instead of 1, which means that the command blocks are running in a different order. The order should be preserved regardless of in which order the chunks are loaded.