It would probably be much more cost effective for the US to pay Chinese firms to reduce emissions (say, by paying for the installation of more advanced filtering equipment) than it is to try and wring further reductions out of US firms.
If we're talking about reducing CO2 emissions, then yes, further cutting emissions in the US is probably not going to do much good compared to putting similar effort into China. But CO2 is just one piece of the puzzle, and it's one which can even be at odds with combating other types of pollution in some cases (as we saw in the VW emissions scandal).
So better turn off your electronic devices etc. NOW.
I think it's fair to point out that the US cutting emissions could have a larger impact than China limiting increases (at least on a per capita basis).
I'd wager that you get much more bang for your buck in China. The US is much more efficient at generating wealth from CO2 emissions: our emissions are about half, while our GDP is somewhat larger. China still has a lot of low-hanging fruit when it comes to cutting CO2 emissions.
In any case, per-capita doesn't matter at all unless you want to come at it from a moral angle.
It certainly shouldn't be the only measure that gets discussion.
You said
> I would really hate to see the US loosen pollution regulations because of some weird idea that we shouldn't bother cleaning up our air unless everybody else does too.
which, to me, only makes sense for types of pollution that are shared. Why would anyone think that China's position one way or the other on a strictly local pollutant should influence the corresponding US policy?
But in any case, my comment is true regardless. Even for local pollutants, there will be more low hanging fruit in China.