Matthew, you’ve hit upon one of my pet peeves!
This happens to everything plastic that I put in the DW- tupperware, silicone, plastic cutting boards, everything. I think I posted a few years back that there was no joy in licking a silicone spatula, because it tastes like the dishwasher. The bowl/parts to my food processor also have this problem, it is yet another thing that must be washed by hand.
My dishwasher is a bosch, not the most expensive one but should be good enough. I also use Cascade complete packets. I do not use any additional rinse aid and I do clean out my filter regularly (I shoot for once a week). The Bosch machines do not have a food disposal (in order to remain quiet) so they do need cleaning. Occaisionally, I even put a little bleach in the drain water in order to sterilize the S curve trap, where there is always water. This makes the diswasher leak in the following cycle (anything alkaline- bleach, soap, etc. does this), but I prepare for it and still do it.
I did use the Cascade packets that come in an unscented option for a while, and there was an improvement, but they didn’t clean as well and now they are not available locally. It does appear to me to be due to the scenting of the detergent, because it changes when I change scent options.
Patrincia posted a long time ago that she didn’t think that Pampered Chef brands of spatulas retained odors, I haven’t tried them to see if they are any different. I have spatulas from a bunch of different manufacturers and they all do the same thing. Call me obsessive, but I reserve spatulas for specific uses and hand wash. I have one for bread, one for chocolate, one for vanilla/light flavors, and several more that are reserved for savory (pesto, etc.) And when it comes to strong flavors like chili peppers or raw garlic, I don’t let them touch anything that retains odors- only glass and metal (plus one reserved cutting board).
I baked deep choc passion cupcakes once in silicone cupcake pans that had run through the dishwasher only once, and I had to throw them all away, they were strongly flavored by that dishwasher smell/taste, so silicone pans are out for me.