The thing is, Democrats who offer public condolences in the wake of public tragedies often also say something along these lines as well (a lot do omit the specific phrase though) and most don't immediately start calling for increased gun control legislation until a few days later at least.
Take a look at the initial tweets re: Parkland that came from four Senate Democrats who are almost all certainly running for President in 2020 (so we should expect them to be the most vocal on the issue).
Gillibrand and Harris offer nothing more than vague platitudes about addressing "gun violence". Klobuchar doesn't even talk about guns and Booker's most hard-hitting line is "Our nation must act." These aren't exactly calls to arms for specific policy proposals, and are really just their own, Democratic version of "thoughts and prayers".
The Left's takes issue with the phrase "thoughts and prayers" because it allows them to ridicule religion and paint Christians as insensitive, uneducated, vacuous individuals. This sentiment is obvious when you read what Democrats like hurricanehink just posted above me.
