A nuclear arms race in Asia is more of a threat to China than to the US, who is on the other side of the world. For this precise reason, I do not see China abandoning its minimal deterrance policy.
Japan and South Korea developing nuclear weapons and be a red line for China, but I don't really see India as anywhere near enough of a threat to be worth considering for China when considering whether or not to expand its nuclear forces.
If anything, getting India to go on a nuclear arms building frenzy now could very well be in China's best interests.
Indian warhead and missile technology is primitive in comparison to China's. But they are improving all the time. Getting India to double down on building masses of inefficient (heavy) nukes and short ranged missiles would not only deplete India's limited materials stockpile (which would be hard to replenish with China torpedoing American strong arming attempts to get an India sized and shaped exemption applied to the nuclear suppliers' group rules); but also saddle the Indian economy with the big burden of paying for the initial purchase, and subsequent maintainance, security and ultimately decommissioning costs of all those missiles and warheads.
It was for similar pragmatic reasons (but reversed) that China settled on its minimal deterrence strategy in the first place.
However, with China's current economic and technological standing in the world, that is no longer a position China needs to restrain itself to if it chooses.
With modern, MIRV warhead technology and DF31/41 and JL2 missiles coming online, Chinese warhead and ICBM technology is very much at long last in the same league as the best the US or Russians have to offer.
China would not need to or want to build anything like the thousands of missiles America and Russia currently fields, but it could very easily and comfortably double or vein triple its current nuclear forces to allow it to attain true MAD with both Russia and America without worrying about the costs or accept significantly inferior performing missiles and warheads.
I think the main thing stopping China is that China seems to be largely optimistic/pragmatic about the future, and don't think all out nuclear war will break out, and/or reason that if it does happen we are all toast irrespective of how many nukes China has. So would rather spend its money on weapons it might actually need to use in a war it can walk away from the victor.
However, I agree that the relentless American moves to counter ballistic missiles is seen as a real, clear and pressing threat to China's minimalistic approach to nuclear deterrence.
China's leaders will not forget the fact that America is the only country to have ever used nuclear weapons in combat, and against a foe without nuclear weapons to boot. So there can be no rose tainted sunglasses view about the willingness of America to use nukes if they think they can get away with it without taking nuclear hits in reply.
That will force China to take a real hard look at whether it's current nuclear force levels would be sufficient to withstand a hostile first strike and still be able to overwhelm enemy multi-layer missile defences, now being deployed right on China's doorstep.
in my view, we can expect China to quietly significantly raise its nuclear stockpile in the coming years.