IMHO there are likely 10 other things in your system that need far more attention. I have heard DACs with intentional sound differences using tubes, and I have heard DACs that allow you to change the filter settings that causes an apparently audible difference which you may or may not like.
Changing filter settings can definitely be noticeable. I believe it is done through phase shifting but I could be wrong. But yes, it is technically a "HiFi effect" or coloration.
I also agree that it can be very difficult to tell differences between very well measured Delta Sigma DACs. Good luck finding audible differences between a Benchmark DAC3 and Topping D90SE.
Some people say that DACs are a solved problem. This is true only if you believe the goal is faithful reproduction of the original signal. Personally, that is not my goal and that is why I am a member of Club R2R ;-)