Considering how Senate Republicans blocked President Obama's Supreme Court nominee for almost a year, Democrats are simply following their precedent now that the Presidential shoe is on the other foot.
I say go for it. Obstruct as much of Trump as you can, but particularly Supreme Court nominees, because the high court is the one obstacle stopping GOP efforts to dismantle critical LGBT and other civil rights.
Some might say this only perpetuates the Washington gridlock, but quite honestly, tough shit. Lives are at stake here. Republicans lost the popular vote for the Presidency, and they received fewer votes nationwide for both their Senate and House candidates than Democrats.
Republicans gamed the system through voter disenfranchisement and gerrymandering so that they could control Washington even though they receive fewer votes. Democrats are simply standing up for the majority that didn't vote Republican nor vote for Trump.
Block them as long as it takes.