I've been round and round in circles with this issue over the years. For a very long time I was one of those begging the councils wherever I lived to recycle, after seeing how well it was done in Germany - but no joy. When the UK finally woke up to recycling, it became immediately apparent it was a mess. Some councils were simply offloading the recycling (sending it to other countries which may - or may not - have then recycled it). Some councils were sending the recycling to manually-sorting centres. Some were sending the stuff of automated recycling centres. Some, commendably, were recycling as much as possible themselves and even distributing and/or selling some of the results (for example compost). In many cases (such as ours) it's impossible to find out exactly what is happening to the 'recycling' and so know how to deal with it in the home.
With our (rural) council, I've had to give up. I can't get a straight answer as to what is happening to the recycling so I simply don't know how to deal with it. I do my best, but it's not easy - particularly given that we have our own, absolutely finite, water supply so we can't waste a drop or we will simply be without water until the next very heavy rainfall.
So I rinse, but don't wash, most things - but definitely not the infamous peanut butter jars. Olive oil bottles go into the recycling without washing as they don't smell anyway. We don't have a dishwasher, and we wash up under running water (if done properly, this takes least water of all - I learnt this in my time in the Australian Bush). The biggest throwaway 'sin' is the containers for the cats' raw meat: they just have to be thrown away because it's not safe to wash them up in the sink (we don't eat meat ourselves) without a huge clean-up afterwards which would be very wasteful in itself.
My main response to the recycling thing is to use as few containers as possible. I make as much as I can from scratch (for example yoghurt, stock, baked beans) and buy bulk. Shopping is not supermarket but Abel & Cole, which is all return-for-reuse packaging. I don't buy any tins at all (actually because of the Bisphenol A factor) and things like passata and anchovies are bought in jars which are rinsable. This is the way I've chosen to tackle the problem, for lack of useful genuine information about recycling.
Finally, I decided I had to stop stressing about it. I do my best; I'll change if/when I receive information which lets me know that I could be doing something in a better way; ultimately there's nothing more I can do.
However, if I meet our Council's Head of Recycling or whatever on a dark night in an isolated rural lane, I won't be responsible for my actions...