In disentangling the question of religious liberty it seems useful to distinguish four typical cases of coercion:-

(1) Coercion by the spiritual power of the baptised

(2) Coercion by the spiritual power of the unbaptised

(3) Coercion by the temporal power of the baptised

(4) Coercion by the temporal power of the unbaptised

It is a matter of faith that (1) is licit. According to the 14th Canon of Trent on baptism, the baptised can be coerced to a Christian life by certain penalties, other than by simple refusal of the sacraments. The present Code of Canon Law allows for certain people to be deprived of their jobs or confined within a monastery as a punishment for heresy. In a Catholic society, the bishop could call on the civil power to help enforce such penalties. That would, however, still be an example of coercion (1) in my schema, since I am considering who the prime mover is in the coercion.

(2) is generally illicit, since the unbaptised are not subject to the jurisdiction of the Church. Nor can she ask the civil power e.g. to freeze the bank accounts of Muslims so that they will be induced to convert. However St Thomas believes that the Church has the radical power to deprive independent pagan rulers of their jurisdiction over the faithful (IIa IIae 10,10), only she doesn’t use it, so as to avoid scandal. He says that the Church has the radical power to do this, ‘having the authority of God’, and pagan rulers have merited  – since they would not even be negative infidels without some mortal sin – to lose their dominion. I am not quite sure how this fits with the idea of baptism as what gives the Church jurisdiction over people. Perhaps one could say that she would not be exercising her own jurisdiction, but being a pure instrument of God’s jurisdiction. In any case, it is purely hypothetical, as St Thomas explains, never being done ‘so as not to scandalise them’.

(3) appears to be illicit in the sense that the civil power cannot legitimately impose penalties for heresy, schism and apostasy except at the will, implicit or explicit of the ecclesiastical power. From the very fact that the spiritual power is higher than the temporal power, the latter must yield to the former when they deal with the same subject-matter.

(4) is perhaps the most controversial point. St Thomas teaches (IIa IIae 10,11), in words that are used by Leo XIII for discussing the same subject, that the rites of pagans (the Jews are a special case) are per se to be suppressed because they are sinful, except when this would lead to some greater evil or prevent some greater good. But from whom is the initiative to come, ecclesiastics or politicians? Since the pagans would be under the jurisdiction of the latter, it would seem to come from them. The civil ruler is the one who has the charge of the temporal common good, and so it seems to be he who must decide, e.g. if a small group of Muslims who have taken refuge in his Catholic country after a civil war back home should be allowed a mosque or not. The question then arises of how a refusal by the civil ruler of the Muslims’ request would square with Dignitatis Humanae. I think it can do if you take into account the clause about ‘public morality’ in DH as a reason to limit religious liberty. In the actual order of providence, every non-Catholic cultus tends to weaken the clarity with which the average citizen, not specially firm in the faith, grasps the truth of the Catholic Church as the one ark of salvation; which surely is a ‘moral’ truth, and therefore a matter of public morality. Only, unlike the case with (1), the civil rulers here cannot aim at coercing the beliefs of the pagans, since, as DH teaches, no merely human power has jurisdiction over the conscience as such.