Russia is said to be involved in the manipulation of the elections and politics of various countries in the West.
Did the West ever manipulate Russian politics?
Is the West able to manipulate Russian politics nowadays?
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Your question is problematic because of the stated and unstated assumptions in it. Russia certainly complains about foreign meddling in their affairs.
The West claims to be convinced that their actions are legitimate in international relations, and nothing like the "underhanded meddling" of the Russians. The Russian government appears genuinely concerned that the West is formenting yet another color revolution in Russia. One might ask why the West doesn't do things like botnets in VKontakte, but it would be limiting to retaliate exactly 1-to-1.
Russia does not have free and fair elections; consolidation of power by Putin appears to be very solid.
Not only can the Russian government take action against media agencies it doesn't like, the ability of a Western-backed faction to actually do anything is limited - they wouldn't be allowed to win elections, and in the extreme might simply be murdered (qv Salisbury).
To some extent because, without a clear need to do so, a blatant manipulation of Russia's "elections" by Western politicians would carry political risks to those Western politicians and would be considered dangerous adventurism by Western electorates. Encouragement and deniable covert support for opposition would be OK but is likely to be of limited effectiveness, as per @pjc50's answer.
Not to mention that support for one politician over another by foreign countries can have the opposite effect to that intended, instead strengthening "foreign enemies" memes used by a government to stay in power. Note that Russia has usually been careful to sow dissent, rather than back any particular politician too obviously. This is not always the case however, see the LePen loan story in France
i.e. this type of action is considered bad form by Western voters. Sure, it happens, but it doesn't do well when thrown in the spotlight, as it would be if Russia was the target rather than say some oil producing third world country.
Edit: not claiming that the West doesn't try to manipulate Russian opinion (they do - see the long list of radio stations specifically set up to do so, along with their Russian counterparts). Neither am I claiming that they don't do anything as underhanded as Russia's Facebook trolls, although we haven't heard of any evidence to that effect. I am saying that Western politicians could expect some major pushback from their electorate if they were caught doing it, which likely tempers the temptation to do so.
Also, at the end of the day, why bother overmuch if you are dealing with adversaries who are fond of censorship? Just pushing out real news, rather than trying to peddle fake news, does the job just as well. If I recall correctly, during the Cold War, the stations trying to influence Russia generally were relatively factual, because that actually worked out in their favor (as opposed to getting caught out in blatant lies). Pure propaganda could be left to Western news outlet addressing Western populations.
The "west" has already "manipulated" Russia and former Soviet states since 1949 with Radio Free Liberty.
Russia Today (RT) was founded and financed by the Russian government to achieve a similar goal.
Regardless of what you might think of both networks. They both serve the same purpose. To influence people in their respective countries. Or in other words, serve as a source of propaganda.