The faithful can obtain partial or plenary indulgences for themselves, or they can apply them to the dead by way of suffrage.
As far as I know, the Catholic Church acknowledges that deceased non-Catholic Christians can go to Purgatory (e.g. this post mentions that Anne Catherine Emmerich had visions of Protestants in Purgatory) so in theory such non-Catholic Christians would be eligible to have indulgences applied to them. Indeed, the Manual of Indulgences describes indulgences as a remission of temporal punishment for sins for a "properly disposed member of the Christian faithful" (as opposed to only the Catholic faithful):
An indulgence is a remission before God of the temporal punishment for sins, whose guilt is forgiven, which a properly disposed member of the Christian faithful obtains under certain and clearly defined conditions through the intervention of the Church, which, as the minister of Redemption, dispenses and applies authoritatively the treasury of the expiatory works of Christ and the saints.
However, the description of an indulgence indicates that it is the Church which dispenses and applies indulgences, so it seems possible that the Church might choose to withhold the dispensing and application of indulgences to certain souls in Purgatory (e.g. Protestants who might have been anti-Catholic in life). Moreover, it's not clear what is considered a "properly disposed member" of the Christian faithful -- perhaps non-Catholic Christians might not be considered "properly disposed" and thus not eligible to have indulgences applied to them.1
Has the Catholic Church explained whether or not indulgences can be obtained for non-Catholic Christians in Purgatory? If so, are there any limitations (e.g. perhaps only souls from certain denominations are eligible, similar to how only Christians of certain denominations are permitted to receive Communion)?
1I suspect the meaning of "properly disposed" refers to the norm that
§1. In order to be capable of gaining indulgences one must be baptized, not excommunicated, and in the state of grace at least at the completion of the prescribed works.
§2. To gain an indulgence, one must have at least the general intention of doing so and must carry out the enjoined works at the stated time and in due fashion, according to the sense of the grant.
However, since I don't see a definition of exactly what "properly disposed" means I can't rule out the possibility that one must be Catholic to be "properly disposed".