How can such damage be avoided? Heavy sweating can cause blue discoloration at the point of contact between the leg and the cello.

It is difficult if this happens over a longer period of time and the color is then really absorbed into the wood or is literally rubbed in by touch. Check your cello regularly at the contact points to see if there is any need for action. The contact points can be cleaned and retouched if varnish is missing.

What can be done to prevent jeans from bleeding so much? For example, you can put them in vinegar water overnight, the ratio of vinegar to water is 1:2.
Or add a little vinegar to the fabric softener when washing.

There are also so-called color-catching cloths in the drugstore that can absorb excess color during washing.