Just to add on to @tcbegley’s comment about specificity, my approach is using the ‘copy css selector’ when right clicking on an element in the browser Dev tool elements section. This of course gives a very unique selector so what I then do is try to take away elements of specificity one by one until I reach that threshold where the dcc style takes precedence.
For example, here is the css selector I used to edit the font of a drop-down for when it is disabled:
Select.control-panel__dropdown.has-value.is-disabled diV.Select-control div div.Select-value span.Select-value-label {
//CSS goes here
}