Do you know which Rabbi (if any) in the Ashkenazi community allows for 1 dishwasher to be used for dairy and meat. I have been told that it is allowed so long as it is not at the same time. I have seen a couple of places where Sephardim allow this under certain circumstances. I have been told that Rabbi Dov Lior allows the use of the same dishwasher for dairy and meat but not at the same time - however I can see no reference to it anywhere. For this to happen then you must clean the filter between the use of it.
Rav Yakov Ariel wrote [www.yeshiva.org.il/ask/?id=4354] that there is no difference between Ashkenazi and Sephardi ruling. He added more that a dishwasher can be used for milk after meat or vice versa if you have separate racks and strainer and run a hot cycle between the two after cleaning the machine.