I believe this is a good example of where we need to exercise the virtue of prudence. So much depends on what the particular resource is, and what these other activities you are talking about.
For example, many of such resources are in the form of podcasts, talk shows, discussions etc., that are more informational or casual or dialectical. It is like playing a radio that I think it is okay to be multi-tasked or disrupted occasionally.
And then there is Christian music, which I suppose you can play in the background while you are engaged in other activities, provided they are not contradictory to our Christian dignity.
And then, some of these are devotional or liturgical, it requires serious attention or has become a commitment in our daily prayer routine. In other words, there are the encounter moments we have put in place at various times of the day to check in with God. This can include online mass, virtual adoration, Rosary, spiritual readings, daily scriptural meditation or nightly examen. We should definitely give our full focus and must not allow ourselves to be distracted.
And then, for the first kind mentioned above, it is one thing to allow ourselves to drive, to cook, or to do other simple chores or even exercise, but quite something else to allow ourselves to be engrossed in secular activities like surfing on gaming, cars, gadgets, or the sort. Again, use your prudence here.