While I think there are a lot of things that make Discovery only so-so so far, I always find this critique a bit odd. Star Trek, right from the get-go, was pushing its generational version of what would now be called SJW stuff. Hell, the original show had a black woman on the bridge along with a Russian and an asian guy. TNG was, oddly, not pushing as many envelopes in this regard but the next two had a black captain and a female captain.
I think if you're only noticing that Star Trek is a show has a bit of an SJW'ey feel to it now you're likely what's different, and you're just more sensitive to the message.
What I find a bit weird is how the showrunners are trying to sell Discovery like it's really pushing boundaries when it's not. What it's doing now is expected and not boundary breaking. Black female leads, gay characters, female heavy cast - none of this is remotely new or shocking in the current year. In fact, it's almost expected to tick off at least some of these boxes these days. TOS and, to a lesser extent, DS9 and Voyager pushed the envelope and helped normalize things that were still not widely accepted at the time. Discovery? Give me a list of shows on the air right now and I bet I can pick five shows doing the shit Discovery is tooting its horn for doing before I'm a tenth of the way down the list. If anything, Discovery is being lazy and playing it safe in this day and age. You want to really push an envelope? Have the captain, who is not being presented as a villain or backwards character, be a conservative Christian white male with exceedingly traditional values which he makes public and colour his actions. That would be controversial these days - not a cast loaded with gay people, people of colour, and women. TOS and even Voyager and DS9 had some guts with their rosters and character makeup - Discovery is playing it safe while claiming it's being risky.