This is a fun question, but could I just clarify where you got the idea of 'states' and the 'Byzantine Republic' from? 'States' were non-existent in the sixth century, since the empire was ruled from Constantinople under an emperor, whilst the latter is questionable because the empire couldn't really be called Byzantine yet, with the Eastern Roman Empire being a better name for it. The 'Republic' bit is interesting though, since the Romans did continue to talk about how great their 'republic' was and how important the 'people' were, even though in reality the emperor/aristocracy's control over military force meant that this was just a veneer. A quick Google search tells me that Anthony Kaldellis will be publishing a book called The Byzantine Republic next year, arguing that the Byzantine Empire was less autocratic than we thought and that the Republican heritage was still going strong, which is a very interesting thesis! Kaldellis is a bit revisionist, but I do enjoy his work, so I'm curious if you got this idea from his works?

Anyway, back to Belisarius. I'm assuming you mean Belisarius' disgrace in 562? He was seemingly disgraced a couple of times, but 562 was the last time he was persecuted. This was recorded mostly in Agathias, who mentioned how Belisarius was implicated with a plot sometimes called the 'Bankers' Plot' (because it was partially caused by the strained relations between the state and the bankers who funded it) (I'm also not sure from where Wikipedia got the idea that Belisarius was accused of corruption, treason is more accurate). Belisarius was not punished harshly and the only thing of note that happened was that his private retinue/household was stripped from him. Belisarius was placed in house arrest and he was back to favour the next year, so in the long-run it wasn't a big deal (he had already been forced into retirement in the later stages of the Gothic War). As Belisarius had saved Constantinople during a Kutrigur raid in 559, I'm inclined to think that Justinian acted leniently because of public opinion. We actually have a panegyric from 562 that, although it didn't mention Belisarius, repeatedly emphasised Justinian's clemency during the re-dedication ceremony of the Hagia Sophia, which may suggest that Justinian was aware that excessively punishing a war hero may be counter-productive.

By itself, I don't think we can really talk about contemporary attitudes of Belisarius or the charges - Agathias was a member of the upper class, whilst the panegyricist mentioned above, Paul the Silentiary, was an imperial courtier. They were both unlikely to criticise the regime, and even if they wished to, they would probably be imemdiately accused of treason and their critiques purged. Remember that the criticisms of Justinian's regime that survived down to us were either written after his death (John of Ephesus or Evagrius for example) or were written in a way that the critiques were veiled. Procopius' Secret History for instance was only to be published when the emperor was dead, whilst John Lydus cloaked his pagan critique of the regime by talking about how much better it was in the good old days of the Republic. Justinian's empire was an oppressive one and recently historians have dismissed the idea of their being a concerted military or senatorial faction operating against the emperor. Instead, there were many impromptu plots (from off the top of my head, I can think of conspiracies in 532, 541, 546, 548, 560 and 562...) that were all stopped before they had any chance of success. Sections of the upper classes were probably angry at Justinian's heavy-handed religious/fiscal/military policies, but we can't narrow down any specific attitudes to the events of 562. More generally, as Justinian's propaganda is the only source for contemporary attitudes, we know very little about what the common people thought about this. From the sources, the public were more inclined to riot about chariot races and religion than persecutions against members of the upper class, though as I said, Justinian was at least worried about what the crowd would do if he punished Belisarius harshly.

Justinian was not exceptionally oppressive though, as his predecessors and successors regularly tortured, executed and confiscated the properties of both the elite and the common man, especially for cases of treason (which emperor wouldn't do that?). So in summary, Belisarius' links to a conspiracy meant that the regime quickly silenced him and put him in house arrest, but because of his popularity, he was not punished any further. Other than that, we have to look at similar persecutions throughout Justinian's reign (and beyond) to get a sense of the people's attitudes - which is that there was a general sense of resentment, but there was very little the people or the elite could do against the machineries of state.