Can I mix cutting boards when I dishwash them

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.

I always considered the advice to be like a second level of defense: Proper cleaning should be enough to make the board suitable for any task. And not everyone has multiple boards, just saying.

However, nothing and nobody is infallible. Using separate boards for various uses helps in the rare cases when something went wrong or someone did a sloppy job. In shared kitchens, color-coding also tells the other users, which boards should be washed especially carefully and which one you shouldn’t absentmindedly use for chopping up a salad just because somehow someone left it out on the counter. The price of an extra board is usually low enough that it’s worth the investment.

So in short:

• Mandatory: No (except for commercial kitchens)
• A good idea nevertheless: Yes.

The main problem with cutting boards and sanitation is that you, well, cut them. Those cuts produce channels where bacteria can hide and survive even a good cleaning. But the main worry is with wooden cutting boards, because of how they get cut (cuts on a wooden board produce deeper more 'cavernous' channels where bacteria can hide) but also because they are harder to wash well and also that bacteria doesn't mind that sort of environment.

I assume, since you said dishwasher safe, that you are talking about those thin silicon boards or something similar. For these it's not a bad idea to use separate boards but it is probably not necessary. They don't tend to have good places for bacteria to hide in the first place and bacteria doesn't survive on them very well, either. Also you can blast them with extremely hot soapy water for an hour on a dishwasher. At any rate, it's incredibly unlikely any bacteria that survived would bounce from one board to the other so I wouldn't be worried about storing them together.

Finally, keep in mind that by far the biggest issue is with foods that are not cooked. So my biggest worry personally would be doing something like preparing a salad on a wooden cutting board that has also been used for cutting raw meat. It's just not worth the risk, even if I knew the board was cleaned as much as possible. I still use separate silicon boards, but that's more for caution and so I don't have to worry about whether the board was perfectly cleaned or not.