Certain usage of "shite mo ii"

In a manga, a young man is attempting to assist his older brother with a shrine ritual. The young man is having trouble remembering when to bow and what to do during the ritual but does not say anything.

The older brother turns to him and says: 「別に長く礼をしてもいいんだよ？」
The young man says: 「そういう問題じゃなくて。プロっぽくないっていうか」

I understand そういう問題じゃなくて as "that's not the problem," but the first sentence has me confused. I'm familiar with this construction being used to ask permission, but I'm wondering if the older brother is somehow asking if the younger is all right with bowing for so long. I guess I'm just not clear on its meaning.

Thank you for any help.

Having read you explanation of the context, the conversation is not so clear to me. But, I (a Jananese native) suppose as follows:

The older brother turns to him and says: 「別に長く礼をしてもいいんだよ？」
This is not a real question.
’Shite mo ii’, in this case, means simply ‘you can …’, and the question mark used here is not an interrogative one, but a rhetorical one which suggests “Isn’ it the problem?”. (Personally I don’t like the usage of question marks like this.)

So, the younger brother answers “That’s not the problem.”
The young man says: 「そういう問題じゃなくて。プロっぽくないっていうか」

The real point I can’t understand is the last sentence 「プロっぽくないっていうか」.
Do you understand this sentence? What does 「プロっぽい」mean in this context?

You have to remember that manga is subculture.

別に長く礼をしてもいいんだよ？ should properly written as
別に長く礼をしてもいいんだよ。
and it means, "Hey, It's okay to bow (for a) long (period of time), you know?"

The "？" in this case implies that the speaker is "saying" the sentence with the ending tone going upward as you would when asking questions. What I mean is that, if you were to apply musical notes to this sentence, よ is not the lowest note but だ is. And then よ is a slightly higher than だ

This is the way some people write sentences when writing casually such as in texting or Tweeting or whatnot. And the difference is as follows:
〜いいんだよ。(with よ as the lowest note): This makes it sound like he is talking to himself and trying to sort of convince himself.
〜いいんだよ？(with よ as a higher note): This makes it sound like he is making a suggestion to someone, which in this case is to the young man.
〜いいの？: This is a real question, and in this case it would mean that the older brother is asking to the young man, "Is it okay if I....?"

In proper literature, a sentence like 〜いいんだよ。would be compensated by narratives such as "..., said the older brother as if to make a suggestion". But in manga and perhaps drama scripts, the "？" says it all.

I can imagine that the older brother meant to mildly make a suggestion. But the young man, perhaps because he was being a bit nervous, felt a bit pressured by it. Hence he ended up replying with an odd comment, but I find it funny that he chose the expression プロっぽくない. I can fully imagine a young man trying to be smart while saying that. It would probably be funnier if I knew the full context.

Ah, that makes sense. The last action before this exchange is the younger brother taking a long bow, only to look up and see that his older brother has already finished bowing. I should have connected this to the dialogue. An oversight on my part.

Thank you both very much for your assistance.

In situations like this, I've found it helpful to think of
「〜してもいいんだよ？」
as
「What's wrong with〜?」
being asked in a rhetorical sense.

To use the same grammar but with a simpler sentence, say Person A drinks some tea that's been poured, and Person B takes issue with it. In his defense, Person A might say:
「飲んでもいいんだよ」
Literally this means "It's OK to drink the tea," but since he's talking about his own actions, and using the emphatic 「〜んだよ」, the feeling matches up with saying something like "There's nothing wrong with me drinking the tea."

Giving 「飲んでもいいんだよ？」 the intonation of question softens that a bit, but not that much, since it's still not grammatically a question, and still has the emphatic 「〜んだよ」, which is why it comes off as a rhetorical question, and would be closest to, in English, "What's wrong with me drinking the tea?"

It's worth noting that talking like this, with a question intonation for 「〜してもいいんだよ？」 has sort of a young-person/teen vibe to it, and can come across as very casual.

By the way, is the manga written by Seo Koji? He absolutely loves giving his characters dialogue with 「〜してもいいんだよ？」

Sorry, I'm going to ask one more question. In the final sentence, is the っていうか being used as just a "you know" filler (I'm not a pro, you know")? Or is the younger brother "quoting" what he believes his older brother thinks about him ("Are you telling me I'm not a pro?").

Thanks again.

っていうか in this case is a colloquial way of saying とでも言うのでしょうか or とでも申しましょうか.

So in full, the sentence means, "It's not professional, if you would." or an expression closer to the nuance is "It's not professional, sort of."

", you know" kind of fits in too, but this っていうか is more like an expression to show uncertainty of the speaker's choice of words. But in this case, I feel that it's not exactly that he's uncertain, but more that he is shy to say プロっぽくい

By the way, I don't think he's saying "I'm not a pro", but he's rather suggesting that he wants to act professionally and that there is a certain act he wants to avoid because that act is unprofessional. Since we don't have context, I’m not sure what act he's talking about.

The funny part probably is that what he is discussing is not a matter of professionalism in real life. For example, if he's a professional bus driver and wants to park the bus properly, that's a matter of professionalism. But if he's just a young student and all he wants to do is to bow correctly, it's kind of exaggerating to talk about professionalism there, and that would be the punch line.

I see. Thank you for your detailed answer; it's a big help.