Two separate points. First one is the long term development of such systems, as they increase in efficiency and capability. Second of all they dont' want to end up on the wrong side of the BMD wall. They partially see this BMD shield as the union of developed countries against third world hell holes with missiles, and they want to be part of the club.
AND
Given their aspirations with the Air-Space Defense system (and by space I mean outer space) that they are trying to create they seem to consider it possible if not tomorrow, within the foreseeable future. As it stands the A-135M is already capable of seriously hampering if not preventing the Chinese strategic nuclear arsenal from striking Moscow. Given development and proliferation of systems like the S-300VM, SM-3, S-500, etc. with BMD capability they may not be wrong.
For the first, there is a very finite limit to just how efficient a BMD interceptor can become. In this case, an accuracy of 1:1 vs. inbound warheads (or missiles if close enough/fast enough to interceptor during boost phase). If Russia has 2,679 nuclear ICBM warheads, and sufficient missiles to far that many warheads (nevermind decoy warheads, countermeasures, etc) then a minimum of 2,679 interceptors would be required to intercept all inbounds. This is of course assuming that all interceptors work properly, do not miss, etc. Given the substantial cost for such interceptors, as well as the level of forces required to maintain such numbers of interceptors, particularly on a hotpad/ready launch status, as well as just the amount of space required to act as launch sites, there is no real way which the US or NATO could hide that level of military activity from Russia.
With respect to Russian concerns about being on 'the other side' of the BMD wall, that does not quite sound right to me. In part due to the ABM system already around Moscow, as well as the work already done on systems like the S-300, S-400 and offshoots which can/would lend themselves to BMD. It seems to me that Russia is already traveling its own road to a (Russian) domestic BMD capability. Granted, the following is IMO, but if Russia was truly concerned about the threat of ballistic missiles from rogue states like Iran, North Korea, or any similar future nations, then I would think that Russia would be lending more economic, diplomatic and military pressure against such regimes to discourage them from developing or expanding such missile capabilities. In addition, I would also think that Russia, if it really wanted to be included in a 'Western' BMD shield, would not have offered sites for ground-based early warning radars, but also wanted to be able to 'shut off' the sites in the event of a dispute with the West. Given the energy dispute which occurred in the last few years about the energy/natural gas flow from Russia to Eastern and Central Europe, I would certainly understand the reluctance on the part of NATO to involve Russia in any way where Russia could potentially disable the BMD
As for China... I admit, the number I had on the PRC nuclear arsenal is a bit dated, and also there is the whole mystery on just how much the PRC is spending on defence, and what items within defence are being purchased, upgraded or replaced. However, 10+ years ago the estimates I have come across was that the total PRC arsenal was only ~100 warheads of all types, and that there were only a limited number of systems (and warheads) capable of long-ranged delivery. I would certainly expect that all such numbers are likely to have climbed in the past decade+ since that figure came out, but IMO there would still be a decent chance that Russia could intercept any PRC ICBM's capable of reaching Moscow, nevermind the literally scorching counterstrike which Russia could deliver.
Incidentally, I am still not a big fan of BMD systems, since IMO they are still not the best or most likely delivery systems a rogue or non-state actor would use to delivery a nuclear warhead to a target. If interested, I will consider discussing what/how I see such devices being delivered via PM or email with a select group here at DT. It is not something I will discuss in 'public'.
-Cheers