As king of the Polish-Lithuanian Commonwealth, Sigismund III added Sweden to his domain and was intent on adding the Troubles-stricken Russia to it too, but from what I can gather, in Sweden, Sigismund III began constructing Catholic schools and placing Catholics in high positions (in contravention of a promise to not infringe on the religious freedoms of the mostly Lutheran Swedes). This would eventually cause a civil war within Sweden, followed by an outright war between Poland and Sweden, which ended with the destruction of the union between the PLC and Sweden.
During the Polish-Muscovite War which took place during The Troubles, he came close to placing his son on the Tsarist throne, but was outraged when one of the conditions of sympathetic Russian nobles for their support was the conversion of his son to Orthodoxy. In retaliation, Sigismund III proclaimed himself Tsar, eroding what little support he had among the Russian population.
So why on Earth was Sigismund III so intent on spreading Catholicism to the PLC's new or prospective territories, even when it was clear the people did not want to be converted from their own religions?
I am mostly familiar with this from a swedish perspective, so if someone can pipe up with the situation in the PLC that would be great!
It's important to mention his family history: Sigismund was the son of king John (Johan) III of Sweden (back when he was still duke of Finland before he overthrew his brother... It's complicated) and Katarina Jagiello, of the famous Polish dynasty. John's father (the famous Gustav Vasa) had ended up giving his sons significant duchies within the kingdom (with his elder son Erik becoming king) various issues, including Erik's possible mental illness lead to John and his brother Charles overthrowing Erik, with John becoming king, but Charles retaining his own semi-independent duchy. (this would be important later) Sigismund was raised as a catholic (with the clear idea that he might become a candidate for the polish crown some day) and seems to have been genuinely personally devout.
As a young man he was sent to Poland to take part in the election, at least early on he seems to have been fairly isolated, and many of his friends and allies were churchmen. There were plenty of complications, and there were at least a couple of points where John argued for Sigismund to simply abdicate, since he felt the poles were treating his son badly. Eventually (and partially due to the support of the Pope himself) Sigismund managed to stabilize his position in Poland by the time of his father's death.
So we had a definite personal devotion, as well as political expediency (the catholic party in Poland had proven among Sigismund's stronger positions) to that fact we have to add the complication religious situation in Sweden, while Gustav Vasa had steered the country towards protestantism, it had at first been a fairly mild one (similarily to Henry VIII he was mostly interested in acquiring the riches of the monasteries) and so the actual doctrinaire conversion had been somewhat inconsistent (and mostly taken care of by lower-level clergy, with the king mostly being interested in institutional control) John III was also somewhat of an ecumenical, wanting to restore christian unity in response to all of this strife, he also seems to have favoured catholic liturgy simply from an aestethic point of view, and of course he was trying to curry favour with the catholic poles and the Pope and Emperor, because his wife had claims to lands in Italy that he hoped to acquire. Part of this involved John coming out with a new liturgy which was meant as a compromise (as these things go, it of course angered both catholics and protestants) as well as more direct negotiations in trying to figure out some kind of compromise. Part of this included some leniency in the area of catholics living in the country: the Queen of course had her own catholic priests, but a few other jesuits, were also allowed to work in the country. This was a complicated affair, and to add fuel to the fire John's brother Charles took a hardline protestant position, and refused to allow the new liturgy in his duchy, which obviously made the entire situation quite messy. John eventually had to back down a little, but his tolerance remained in force during Sigismund's reign.
As you might see the swedish situation is complicated, and the religious questions were to some extent used as clubs and propaganda by Duke Charles and Sigismund's other domestic swedish enemies. Sigismund's religious policy was by and large similar to that of his father (at least in Sweden) and while he probably hoped for an eventual return he never took any official steps to do so.
Duke Charles gradually strengthened his power, and after a brief civil war Sigismund was deposed as king of Sweden (starting a long series of complicated wars between the two countries)
The complex issue is that Sigismund's legal position in Sweden was arguably stronger than in Poland, but since he had to remain in Poland all the time that gave plenty of room for Duke Charles to outmanuever him.
The loss of his swedish crown seems to have further entrenched his catholic sympathies (partially as he had less reason to cater to the protestants without the need to keep his swedish crown) and it is likely his insistence on allowing his son to remain catholic was in part in order to avoid having a repeat of the situation in Sweden (where the unclear status provided space for political opposition)