After the Battle of Klushino, Polish troops entered Moscow. The Boyars of Russia then elected the heir to the Polish throne, Wladyslaw IV, as Tsar. However, his father, Zygmunt, demanded that he himself become Tsar, which led to a popular uprising in Russia against the Poles. What if, instead of getting greedy, Zygmunt negotiates with the Boyars and agrees that his son will remain Catholic but Orthodox will not be threatened in Russia? Is there a Polonowank, or does Poland simply take the historical role of Russia in history? Or does this prompt a war with Sweden that is disastrous for all involved?
Firstly, there was significant armed opposition to the Boyars' government, and popular uprising would be almost inevitable, irrespectively to the Tsar's person (but non-Russian, and especially non-Orthodox Tsar would be especially vulnerable).
Secondly, there was almost total breakdown of authority in Russia, so any Tsar would need to build his regime almost from scratch, and I'm not confident that young and unaccustomed to Russian politics Wladyslaw could be such regime-builder (I remember his defeats in Polish politics at the end of his reign in OTL).
Thirdly, every Russian noble knew, that election of Catholic Polish prince to the throne of Moscow meant future union between the Polish-Lithuanian Commonwealth and Muscovite Tsardom, and they were strongly against such union (inferiority complex, so to speak, plus religious prejudices). The Boyars needed Orthodox Tsar namely because such Tsar would be ineligible for the Commonwealth's throne (not legally, but politically so).
Promise of toleration for the Orthodoxy in Muscovy would be vastly insufficient - that religion was in the position of total domination in the Tsardom, and only continuation of such situation would be sufficient to maintain Wladyslaw's power in his new realm.
So, if Muscovy received Orthodox Wladyslaw, he would have some chances to retain the throne, but there would be two different states with related monarchs - the Commonwealth under Zygmunt (and later Jan Kazimierz) and Wladyslaw's Muscovy. Relations between these states could be friendly or inimical - it depends on their elites' interests, but, of course, there would be potential for sustainable Slavic alliance against Sweden and Turkey. Such alliances existed in OTL - Holy League in 1686-1700, for example.