Thanks for your question! Back in 2020 I answered the question, “Is it a sin to watch R rated movies?” and that answer has a lot of similarities to the answer I will give you. The short version of this previous Ask The Pastor question is this: The Bible doesn’t specify which ratings we should be watching or not be watching. But as a new creation, saved by Christ and call to a higher standard, we are called to purity and godliness. Therefore, the responsible path is to choose to put things in front of us that reflect godliness, not mock it. This refers to all Christians, not just pastors.
Regarding your question, I don’t know if you are referring to a sister in a family sense or spiritual sense, but the answer is the same either way. We are called to pursue purity and godliness. Watching immorality in movies does not help us with that goal, whether that is with someone or not. So while it may technically be “permissible” (in the sense that there is no specific command against watching profane movies) it is certainly not “beneficial” (see 1 Corinthians 6:12, 10:23).
But there is one additional element you bring up. The person you are asking about is a youth pastor.
A “pastor”, whether he is working with youth or any other group, is someone who, by definition, oversees and shepherds. He would certainly be seen (among other things) as a spiritual role model to be looked up to. In the Bible (Titus 1 and 1 Timothy 3), we see that pastors are called to a higher standard. To be a pastor you must be a faithful husband, slow to anger, above reproach, etc.
If a pastor were to encourage someone to watch a particular movie, then they are endorsing it. Maybe not all the actions in the movie, but at least in general terms. And a pastor who is endorsing sinful actions by watching these things or encouraging others to watch them is completely missing the mark as a pastor! Not only is that NOT above reproach but doing these types of things is also totally neglecting the duties to shepherd.
Would a police officer be a good officer if he went around encouraging people to break the law? Would a car salesman be doing a good job if he actively tried to send his customers to another dealer? Would an elementary school teacher be doing his job if he occasionally mixed in incorrect instruction? No to all of these! Likewise, a pastor would not be doing his job if he encouraged others, particularly young folks, to engage is watching/endorsing sinful activities.
So to answer your question, it is a horrible idea for youth pastors to watch “mature” content with young folks.