They don't savage members of their own party. If you have an example where they have I'll be glad to consider it.
Jon Stewart killed Paul Begala (and Tucker Carlson) famously on CNN's Crossfire. Begala is one of the most recognizable faces/names from the Clinton administration. https://www.youtube.com/watch?v=aFQFB5YpDZE
Stewart has repeatedly stated that he thinks Democrats are ineffectual and incompetent at getting any policies passed (examples: Larry King interview, Terry Gross NPR interview and one of my favorite Stewart quotes ""It's not that the Democrats are playing checkers and the Republicans are playing chess. It's that the Republicans are playing chess and the Democrats are in the nurse's office because once again they glued their balls to their thighs.")
Stewart went after Obama over Libya last month: https://www.theblaze.com/stories/the-critics-are-lining-up-now-jon-stewart-attacks-obama-over-libya/
Colbert is tricky because he's playing a character so any "criticism" of Democrats can be dismissed as part of the performance. However, I do remember that he went after particular Democrat Senators on the health-care debate. https://www.examiner.com/political-...senate-democrats-who-killed-the-public-option
These are just from memory running only google searches based on things I personally remember. I'm sure I could get you dozens if I did this in any systematized way.
But this is actually proving two different points:
1) That they do criticize members of the Democratic party; and
2) unlike the other people they were compared to, approval from Stewart and Colbert isn't a functional litmus test for suitability for office.