Many suspect that Kirill is the Kremlin's cleric, intent on advancing a pro-Russian agenda.
The accusation is that his presence will precipitate the looming schism among rival Ukrainian Orthodox churches.
However, one of the key priorities of Kirill's patriarchal reign is to improve relations among Orthodox churches weakened by divisions and conflict.
These divisions have a long history, but tensions flared up in the early 1990s when the Soviet Union collapsed and was replaced by newly independent states that sought to bolster their autocephalous national churches, with their own patriarchs and full jurisdictional authority.
Since then, Ukrainian Orthodoxy has been split between those who pledge loyalty to the Moscow patriarchate and those who seek to establish a fully independent body under the aegis of the Kiev patriarchate, which is considered schismatic by the Russian Orthodox church. Kirill's visit in the Ukraine seeks to avoid a full-blown schism.
The Ukrainian scenario encapsulates a wider problem across the Orthodox world – tensions between the Moscow patriarchate that accounts for almost half of around 270 million Orthodox faithful and the other national churches.
Some, like the Kiev patriarchate, refuse any links with the Russian church and lack any external recognition. Others look to Constantinople – the cradle of Orthodoxy – and its ecumenical patriarch who enjoys the status of "first among equals" (primus inter pares) within the Orthodox episcopate.
Yet others accept the Moscow patriarchate's traditional claim to pre-eminence over the other Orthodox churches. Since the demise of the Byzantine empire, Moscow has often arrogated to itself the dubious title of "Third Rome" – the sole legitimate successor to the legacy of Roman empire in the west and the Byzantine empire in the east.
Pointing to the proximity between the Moscow patriarch and the Kremlin in the post-Soviet era, critics say that this sort of messianic faith fuels both Russian religious supremacism and political imperialism.
The trouble is that in modern times most, if not all, Orthodox churches are predominantly national communities that support and serve the sovereign state – a marked difference with the transnational Roman Catholic church led by an independent pope who does not owe his authority to any secular power.
For complex historical reasons, the ecumenical patriarch of Constantinople (now Istanbul) has to be a Turkish citizen resident in Turkey, giving the republic's strongly secular influence over internal church affairs.
By forging closer links with other Orthodox churches, Kirill is determined to reassert the trans-national character of Orthodoxy. On his first visit as patriarch in Constantinople at the beginning of this month, he appealed to the common theological tradition that binds together the Orthodox sister churches.
Crucially, he also described the ecumenical patriarchate of Constantinople as the new Rome that safeguards the unity of all local communities across the Orthodox world.
As the head of the single largest Orthodox church, Kirill's desire to defend the special contribution of the Moscow patriarchate "to the common Orthodox witness before the modern world which is losing its spiritual and moral guidelines" is not reactionary nostalgia.
Rather, it underscores his continued commitment to a shared supranational Orthodox identity.
Nor is it accurate to brand him as a Russian neo-imperialist dressed in the clothes of religious piety. Like his predecessor Patriarch Alexy II, under whom he served as metropolitan in charge of ecumenical relations, Kirill has already improved ties with other Orthodox churches.
Last summer, he opposed the creation of a new patriarchate in Georgia's breakaway region of South Ossetia, arguing that political independence is no reason for the South Ossetian Orthodox church to cut ties with the Georgian patriarchate.
(Both the Moscow and the Georgian patriarchs spoke out publicly against the military conflict).
Kirill's visit to the Ukraine is of a piece with the logic of Orthodox unity rather than an ill-conceived exercise in pro-Russian PR.
Key to a stronger pan-Orthodox identity is greater church autonomy from the state – Kirill's other key priority. In a sermon during his enthronement service attended by both President Medvedev and Prime Minister Putin, he criticised the Russian government's response to the current economic downturn, enjoining the president to take bolder action and inveighing against the authorities for violating the standards of justice and righteousness.
Moreover, only a fortnight ago Kirill obtained guarantees from Russian politicians that the Moscow patriarchate would be allowed to preview all legislation considered in the State Duma, Russia's lower house of parliament.
This extraordinary agreement enables the church to examine proposed legislation and influence its outcome. Staunch secularists and atheists will be up in arms, but this is potentially a stunning reversal of the widely perceived subordination of the Orthodox church to the Russian state.
None of the patriarch's initiatives are uncontroversial, but the charge that he is the Kremlin's cleric simply doesn't wash. At 62, Kirill is relatively young and his patriarchal rule could last for a generation.
Together with the ecumenical patriarch of Constantinople and others, he will seek to strengthen Orthodoxy against the forces of aggressive secularism and atheism and to affirm the autonomy of the church vis-à-vis the state without divorcing religion from politics.
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