There I think you need to distinguish Democrat from liberals/leftists/progressives. There are differences of opinions among the latter group. I would say the majority distrust the police and the military but see them as necessary institutions that should be reformed. The
Democrats, which is to say the people who have some claim to speak for the party, profess their love for law enforcement and the military, whatever their private reservations. This is not how Republicans, the politicians, behave towards the EPA and the rest.
Also, the Democrats have never had a politician of any stature, let alone a president of their party, say "Government is not the solution to the problem. Government is the problem." That was Ronald Reagan.
In other words, you are right, the left does distrust those portions of the government it does not control, but there is an enormous difference of degree in how the two sides behave towards these portions of the government.