That depends on the scenario we're lining out.
If you look back a few posts, I put up the scenario a certain island is declaring formal independence and china moves to blockade it with its navy, and warns the entire world (i.e.: the US) that if foreign military vessels come within a set distance (a few hundred kms lets say) such an action will be interpreted as hostile. (Tbh this is the most likely scenario in which the US and PRC can come into conflict for the forseeable future -- taiwan is the highest flashpoint, though you can replace it with a south china seas dispute which would work as well).
At this point, the US wants to send in carriers, but the chinese have repeatedly warned about their DF-21D (and submarines, YJ-62, 022s) will be used against said carriers if they move into the "demilitarized zone".
If the US attacks chinese satellites or OTH stations then it'll amount to a declaration of war anyway, so while it'll be harder for the chinese to use DF-21D to sink USN CVNs, you can expect massive casualties on both sides from the sh*t which hits the fan after -- which could easily amount to greater men lost than the few thousand of hands on a carrier.
Then it becomes a question of simply who's better... jeezus no one's saying it'll be easy (or that it's been easy) to put DF-21D into a workable system.
And I think many people are thinking about the actual military details too much -- the simple fact that there is a DF-21D, among the PLA's other A2AD weapons like the 400km YJ-62 AShM, 022s, and AIP SSKs all linked up with a future informationization network, means the US will have to really comprehend the consequences of sailing in the far westpac in a time of high conflict.
In the scenario I lined out above, if taiwan did declare formal independence and the PLAN did move to blockade it, the USN would certainly move in with carriers without a second thought if weapons like DF-21D, YJ-62 SSKs etc didn't exist. But the fact that they do, and that they have the potential to inflict massive casualties on the US side means the US will have to think twice about just how much they value the [sarcasm]freedom[/sarcasm] of taiwan. Sure the US can go ahead and say well we're going to attack your satellites, and OTH stations before we move our carriers into the "demilitarized zone" so it'll be harder for you to track our ships and thus fire your missiles -- but such an act will be equal to declaring war anyway, and in such a conflict between the US and PRC the theatre will be greater than just the seas around taiwan -- in other words, expect massive casualties on both sides. The Chinese public all see Taiwan as something that they are willing to fight for, how about the US public? Having fought in two long, draining wars in the 21st century and now fighting against their nearest peer not to mention banker? Unless you conjure up some major china-hate to overlook the losses and the two country's economic relations I can't imagine the public standing for another war. Because people love to go to war if they can win easily, but start getting butthurt when they see the fight is actually costing them.
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If the reply to what I said above is "well the US is going to attack chinese satellites and OTH radars anyway to make it harder to fire DF-21Ds even if it means all out war" -- fine then, but by that point all bets will be off anyway.
DF-21D is as much a strategic psychological weapon of deterrence as an ICBM, B-2, or indeed an american super carrier is.
