Keep eating nuts and seeds, but delay processing as late as possible.
The process of slicing or grinding nuts increases the surface area of nut which is exposed to the air, and that accelerates the process of oxidative rancidification. It is best to store nuts whole (either shelled or unshelled) and then process them (eg. shelling, slicing, grinding) at the time they are to be consumed.
Oils extracted from nuts and seeds are the most volatile, because they've undergone the most amount of processing and the oils are now directly exposed to air and light. Lipids (fats) may be bound up to proteins or carbohydrates within a whole food and that makes them more stable, but a refined oil comes from breaking those chemical bonds. Extra care should be taken to store oils properly and ensure they are consumed quickly rather than being left on the shelf.
The nutrients in nuts can be further protected by storing them in a dry, air-tight container kept at a cool temperature in a dark space. An air-tight container reduces potential for oxidation, and cool/dry containment reduces potential for hydrolysis, both of which may degrade the oils in nuts.
Nuts will have a noticeably unpleasant taste when they've gone rancid. If you notice this unpleasant taste, it indicates the nuts may have been stored improperly and you should probably stop eating them. If you don't notice this unpleasant taste, the nuts probably haven't gone rancid so you needn't worry.