Yes, a human problem, but nothing about "this and not that". However, we could get "this and not necessarily that".
First, let's review some of our Greek.
The issue is about "entrusting" (ἐπίστευεν αὑτὸν / episteuen hauton from πιστεύω αὐτός / pisteuo hautos - lit. "believe himself [in them]"). "Entrust himself to them" is a very accurate translation, noting that "trust" from "entrust" is synonymous with "faith" and "belief", all from the same Greek word "πιστεύω/pisteuo". "Himself" is a reflexive pronoun in the accusative case, as we would expect for a reflexive object.
As for pericopes, the paragraph does begin in v23; the previous paragraph began in v13, the cleansing of the temple. The location and occasion is the same: Jerusalem at the Passover.
Remember this is John's Gospel, and the timeline was out of order for the sake of theme-based teaching. Traveling to Capernaeum in v12, then arriving at Jerusalem in v13 is hardly a time-driven narrative. Moreover, we didn't have such a massive following of Jesus at a Passover before he meets the woman at the well in John 4 since she was the first he revealed himself to as the Christ. So, this is a flash-forward. John is setting the previous paragraph in the same larger pericope as having a thematic relationship to this, but as part of the same "flash forward" in which occurs all of that contextual conflict of this question.
So, the question's point about previous conflicts is indeed relevant.
Jesus is still in Jerusalem at the feast of v13 in v23. So, we can consider conflict with Jewish leaders—in the very Temple itself—as not merely conflict with Jewish leaders, but the greatest conflict of all with Jewish leaders. This certainly is part of the conflict.
Jesus not entrusting himself to the masses in v23, however, has an explanation from vv24-25, so we do not need to rely solely on a contextual explanation for v23.
Yes, it's an inherent problem in humanity, even surpassing sin since Jesus knew this problem first hand while not having sin; it wasn't a problem about the immediately preceding conflict. That conflict was just part of a much larger problem.
But, the text doesn't say all of this categorically.
We can't derive the specific categorical "and not a Jewish problem" from this because John doesn't mention "the Jews" in a way for that purpose. But, we can certainly get "and not a Jewish problem specifically—nor any other specific problem for that matter—, but a human problem specifically".
Style of this statement
Moreover, we can see the context of the pericope as further reason for this broader, human problem as the main reason.
With all this conflict in the context, attentive readers will surely ask if that is the reason for v23. But, to remove all doubt, John does what he often does in his narrative and makes a direct explanation in vv23-25. He does this on a larger scale in 20:30-31 as his direct explanation for the entire book.
John 20:30-31 (NASB)
30 Therefore many other signs Jesus also performed in the presence of the disciples, which are not written in this book; 31 but these have been written so that you may believe that Jesus is the Christ, the Son of God; and that believing you may have life in His name.
...clearly explaining his purpose in 20:30-31 is the same type of direct statement as 2:23-25, which this question is about.
The main issue here is almost a lesson by Christ's example for social media "influencers" who have the tendency to lose themselves in the limelight of fandom, as is often the case with any celebrity for that matter.
Having just cleansed the temple, this is supposedly Passion Week, just after his triumphal entry—again, John uses an out of order timeline for thematic purposes.
So, while he is quite the celebrity, he doesn't let it go to his head! After all, he himself knew first hand how humans have desires for personal ambition. While they all lauded him, he knows they will kill him a week later.
Even if we buy the "two-temple cleansing" interpretaion based on a non-synoptic Gospel, it won't change the conclusion, but seeing this as a flash-forward helps set the context even better.