Hubby and I were brought up to always offer to do the dishes after dinner at someone's house. We always ask first and if our offer is accepted, we do it gladly. We appreciate the effort the hosts have put into the meal and we are happy that we are not leaving them with a dirty kitchen.
When people come to my house and offer to help me clean up, usually, i will decline unless i am sick, tired, or have to wake up very early to go to work. I am a neat cook so usually, there are very few pots and pans to clean and almost everything else goes in the dishwasher, and i never let anyone wash something that can be washed by the dishwasher. NEVER. Oh, and I always try to give them a way to back out of doing dishes just in case it had been only offered for the sake of politeness.
Yet, i cannot help but feel that -unless it is an extreemly formal dinner- not offering to help do the dishes is rude. I understand that I invited them and that I am the one responsible for the clean up, but for them not to even offer to help is a bit weird.
Having written this, I realised that I did not mention i am talking about people who just sat down for the entire meal and did not help with other aspects of it (prep, getting dishes to table, clearing table......) I certainly wouldn't think it's rude if someone who helped do prep other things did not do dishes.