Avocados should also be left out, just like bananas to ripe before stored in the fridge. It would be best if kept at room temperature to have the right flavour and texture.
When they are ripe, you can transfer them to the fridge, even though they will not change their flavour or freshness.
Storing ripe avocados in the fridge can also add a few more days to their shelf-life.
Ketchup contains a lot of vinegar that acts as a preservative and does not need any refrigeration. You can even return it to the pantry after opening the bottle, and it will still maintain its flavour and freshness.
However, if you buy low-sodium ketchup, you can put it in the fridge to be safe.
Refrigerating nuts prolongs their shelf-life by preventing the oils from getting foul. However, they easily lose their nutty flavour and assimilate the scents of other foods in the fridge.
To maintain their flavour, you should store them in a hermetically sealed container at room temperature.
If you had stored them in the fridge, you would have to toast them in a dry container before eating.