Obviously with all the woo-woo of hyper-advanced technology we could rationalize even things which seem evidently impossible given what we know about physics, etc. I don't think it will ever be possible, as the energy required to disrupt a massive and relatively stable system like a star (stars may not be stable in the very long-term, but in the timeframe of the game, stars are stable for hundreds of millions, to billions of years. The system is largely self-correcting. It would be very hard to disrupt it to the point where it would collapse or explode, and require a stupid amount of energy. And if we have access to that kind of energy, the notion of duking it out oldschool-style with massive ship battles just seems antiquated. So I feel like the concept fits into the game's setting, even if physically possible given some criteria, but that is just my instinct.
So, should you be able to do this in the game? No, probably not. Mechanically all it does is make the game less interesting by removing parts of the playing field. I realize that some people may like it thematically, but it doesn't add anything to the game, and may conflict with other mechanics (as was mentioned by the possibility of hyperlane travelers being 'cut off' from the rest of the galaxy.
Are there mechanical solutions to possible mechanical problems? Yes, probably.
Could we imagine up some future-technology that could blow up a planet or star? Yes, probably.
Is it worth it? Nah, not in my opinion.