I don't think a new Star Trek
series needs to worry about being a product of our times or make reference to current events, which can be too limiting and run the risk of being obvious and clumsy.
There are timeless aspects to storytelling that always work. The idealistic hero, the implacable foe, the forbidden love, the character with divided loyalties, the anti-hero, the fish out of water...not that I'm advocating any or all of those, just pointing out that elements like that can always be assembled into a good story regardless of what's going on in the world.
The bigger issue for Star Trek
is not what's going on in the world but what's going on in the TV business. There's no really good place for any sort of space opera now. SyFy is doing well with ghost-hunting reality shows, wrestling and cop shows that pay lip service to sf/f. A space opera would be more expensive to produce, and wouldn't necessarily get better ratings.
Broadcast is pretty hopeless now but there's reason to believe that ABC and NBC at least might be taking interesting risks next season. Cable seems friendly to sf/f, with some of the biggest hits (The Walking Dead, American Horror Story, Game of Thrones
) in that genre. There's a massive number of sf/f shows on broadcast and cable in development for next season but only one
is a space opera by any definition. A few others include some alien angle, but are Earth-based.