Why would simple Earth Plantation/Vineyard owners (Picards Parents) stop everything they were doing and change their plans because Vulcan was destroyed? It would have nothing to do with them, they weren't Starfleet, they have a Plantation/Vineyard on Earth. Did everyone in California stop everything they were doing and change all their plans and their whole life because of Hurricaine of Katrina devastating New Orleans? No. Sure some ran straight off to New Orleans to help out, but, most just went on about their business. The destruction of Vulcan would be nothing more than a passing thought, if that, for a Plantation/Vineyard owner
That sounds rather dispassionate. I wouldn't liken it to a natural disaster. It was a terrorist attack that involved the destruction of an entire Federation world. I think the closest modern American equivalent would be 9/11, but in 9/11 there was only a few thousand deaths rather than billions; a terrorist attack vs. genocide.
Now imagine the ways in which 9/11 affected your life. I could certainly say that my specific kids wouldn't have been born if not for 9/11, and I didn't have any direct ties to New York either. I didn't just shrug it off and say, "Well, back to my own little world." I didn't run out and help people either, but it changed the way I thought, and there were many experiences to learn from it, and many things to consider. It also affected government policies, diplomatic relations, the economy, culture, etc. There was a lot of fallout. Even if you kept to yourself most of the time, a lot of the people surrounding you may not have.
Since 9/11 was just a drop in the bucket compared to Vulcan being destroyed, imagine if the entire UK was destroyed. Do you not think that would have any impact on people across the globe? Do you think they'd still go about their business in the exact same way? It's highly doubtful.
Although IRL the known TOS crew united for the movie in 2258, in-universe the crews weren't "correct" for the time. The prime-universe Enterprise crew of 2254 included Number One, Doctor Boyce, Jose Tyler and Yeoman Colt. That's very different from the crew we saw in STXI, which began with Chief Engineer Olsen and Dr. Puri before the TOS regulars took over, and was still missing Yeoman Rand by the end of the movie. The full TOS crew (including Chekov) wasn't united until 2266.
That reinforces the idea that this crew is some crew of fate. Despite other things being so different, what is it that makes it so that they all end up in the exact same places and positions? It's fate.