bilby
Fair dinkum thinkum
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I think jamming/spoofing/temporarily blinding GPS is more likely as long as the US stays out of the war (though I wouldn't rule out taking them out and attacking the US by surprise). But China attacks Taiwan but not the US and the US fights back, I'm pretty sure GPS and generally US satellites would be targeted with many missiles.Angra Mainyu, destroying GPS is an act of War against US and really the whole World.
And at this point it's pointless anyway, because they would have to destroy russian and EU system as well, They can ask Russia to turn it off of course. Taiwan is not worth nuclear war. China has no way get it back without US willingly letting it happen.
(and yes, they would have to block the EU system, or destroy their satellites too; I think Russia would probably turn it off as you suggest).
As for nuclear war, I do not think that the US would respond with nuclear weapons to a conventional attack by China (probably).
The GPS signal strength at the Earth's surface is pretty weak (the signal is broadcast at a power of about 45W, and the minimum range to a satellite directly overhead is in the order of 20 000km). Jamming it locally shouldn't pose a big technical challenge for any military force. Physically damaging the satellites would be expensive, difficult, inviting of retaliation, and (most importantly) unnecessary.