Can I mix cutting boards when I dishwash them I have a dishwasher safe set of boards. I've heard a common advice to use separate boards for meat, fish and ready to eat food. However it got me thinking - I don't mind mixing plates or other utensils as they are cleaned by dishwasher anyway (or hand washing).

Does the advice applies to mixing without cleaning? Or are there reason not to mix despite cleaning?
I'm not sure I  understand the question.  In a cleaning situation, where you are using soap and water, there is no reason you can not clean your boards together. Once you have clean boards, there is no reason they cannot be stored together. The potential issue is cross-contamination.  If there are no contaminates, there is no issue.