Are this white stuff in the avocado roots any illness of the plant?
Should I do anything about it?
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There is a discussion here on Reddit that speculates on what these might be; I think the most likely is the start of new lateral roots. They remind me of the hair roots that form on seedlings when highly filtered/purified water is used in the greenhouse. Maybe they do not do much because they are still in pure water and have no incentive to go exploring further for nutrients.
There are some publicly available images which show the entire root covered in these hairs with a vigorous and healthy set of leaves on the shoot, so the evidence points at this being quite healthy and natural. If you can, examine them under magnification when you transplant to soil and let us know what you find.