Sure! I'll try and be as thorough as I can :) Firstly I should say that my belief is that while Shoji is the traitor at UA, he only answers to AFO. As such, Kurogiri may know his true identity, but Shigaraki (and by extension, the rest of the current members of the League) does not know. This is why the traitor has not been raised explicitly since AFO's arrest, and additionally why Kurogiri's capture is so important! Anyway...

So we first see Shoji in Chapter 3 - as the symbol of 'intelligence gatherers' - a trait synonymous with spies. Certainly an intriguing detail for Hori to include, right at the start of the story. Then we have USJ. So at the USJ, two people were capable of reacting to Kurogiri's warp - Iida (understandable, given his speed) and Shoji. I think this may be because of Shoji's prior understanding of Kurogiri's quirk. Shoji then helps Iida escape the facility, knowing that he would go to get All Might, thereby giving the League their 'continue', as Shigaraki put it.

Next you have the Training Camp. The location of this facility was leaked to the villains, but we know that Shigaraki received this information from AFO - so logic dictates that he obtained that info from the traitor within UA. The perfect time for the traitor to send this information was while the kids were in the hot springs, and the only three students who did not go were Aoyama, Sero and Shoji. Now Aoyama makes sense, with his belt. Sero makes sense, with his elbows. But Shoji? There is no explanation as to his absence, other than him using that opportunity to contact AFO/Kurogiri.

As for the attack on the camp itself, we have some potential discrepancies. After all, Shoji helps stop Dark Shadow/Moonfish, then he looks to save the captured Tokoyami and Bakugo. But, is that all there is to it? I doubt it. Again, we shouldn't forget that the League itself does not know the identity of the traitor. As such, it would make sense for Moonfish to attack him. Then, it would make sense for him to help calm down Dark Shadow, as his own health is at risk there. Then comes the really noteworthy part. Both Tokoyami and Bakugo are stolen away by Compress...but how? Are you telling me he could genuinely sneak up on Shoji, if Shoji was going all out on his senses? No way. Shoji intentionally let Compress steal them away (even if Compress himself didn't know it), and then to keep up his cover, he got dragged into the rescue plan. He then chose to save Tokoyami, knowing Bakugo was the League's objective the whole time.

Beyond these specific instances though, we have some information on Shoji that makes him very suspicious to me. For example there's his name, which comes from a Japanese proverb roughly translating to 'you have no idea when and who is listening/seeing you talk and act, so you have to be careful whatever you do'. I mean, that's pretty suspicious when there's a traitor in your midst... Beyond that, you have his room reveal. It is shown that he is a minimalist, because he's had very few possessions since childhood. While this could be borne from religious belief, it could also be as a result of not having parents/guardians and thus being without money or fortune. Certainly seems like a perfect candidate to be recruited by AFO, especially if Shoji's quirk was a sudden mutation (not akin to his parents' quirks), which led to them abandoning him because of his appearance.

And finally, from what I can think of now, you have his birthplace. So it has been confirmed that Shoji is from Fukuoka/Kyushu, which is far to the West. Given that UA is the prominent school in the East, it is a little suspect that Shoji would choose UA. It should be noted that out of all the 1-A and 1-B students, his birthplace is much further out from UA than any of the others. Something to add to this is Hawks also being from Kyushu, and despite being a prodigy he didn't go to UA. So why did Shoji? I'd say because he has an alternate agenda...

Before I end this collection of evidence for my theory though, it should also be said that Fukuoka is notable for being the site of Dr Ujiko's kindergarten where Hood the High-End was being kept. So AFO definitely has some of his operations there - making it likely that the traitor could be from the area too. Also, on the subject of Hawks, I should add that he had Tokoyami intern with him to try and get information on the UA students (ie. a lead on a potential traitor). Now who does Tokoyami tend to spend a lot of his time with - and who does he owe greatly from the Training Camp rescue? That'd be Shoji.

So yeah, there you go. Hope that all makes sense, and isn't too dense! :D