oil rancidity doesn't cause ill effects in general, just off smells and taste. Which, if you don't notice, is fine, the more things taste good to one, the better off one is.
I think unopened sesame oil can have years of shelf-life. I certainly never had a problem with the smell and we use sesame oil quite a bit in our household.
Same for me - I’m quite sensitive to rancid oil and have never experienced an issue with any brand of sesame oil kept unrefrigerated for a long period of time.
Rapeseed oil is what I use. It can be kept in the fridge, and from what I manage to read online there are no real benefits of olive oil over it except maybe taste and vitamin e content, and people claiming otherwise seem to never really be able to back up their claims.
It works just as well except when you want the taste of olive oil. I find it superior when I stir fry things since the smoke point is higher.
I’d rather recommended only buying bottles of olive oil with printed harvest dates on the bottle within the last year. It’s absurd that stores are selling two year old oil. There’s a real problem with grocery stores having too many options for a single product and then most of the product on the shelves is unacceptably old.
See also: coffee.
We could have better food with fewer preservatives and less processing if the supply chain would pay attention to this problem.
If you buy directly from a roaster they'll always tell you the roasting date, but most supermarkets actively forbid them from putting that on the bags sold there.