I remember that you said that I should not write about this a while back because it was a statistically insignificant event at the time. But, it continued. I asked about why the rally 'round the flag faded. I saw what I thought was a statistically significant decrease in approval from the second half of March to now. The approval of Donald Trump's job from 538 is down from about 43.5% in mid-May to about 41.2% now. Why did it drop? I am looking for a policy answer. Was it George Floyd, the Bible photo-op, or a combination of both?
It's always hard to ascribe any polling movement to a specific action or lack thereof. Polls are a lagging indicator - they can only be asked about things in the past, and they take several days to conduct, so (especially in a time with rapid news coming out) by the time someone gets asked their opinion there have usually been many events that factor into it. People are also very bad at understanding or articulating the source of their own opinions, so asking them a "Why?" question is not generally useful. Finally, there's also rarely any recent "before" polls to compare an "after" poll to, because there are too many possibilities of what might happen - for example, who would have thought to ask questions about policing in April amidst the shutdown of everything?
All that said, pollsters have some tools to get at this information. Just keep in mind that very few opinions are shaped by any one specific item in isolation.
In this particular case, this polling roundup cites two surveys which asked questions about this:
As for President Trump’s handling of the protests, Americans largely gave him a thumbs down. The CBS News/YouGov poll found that 32 percent approved of Trump’s response while 49 percent disapproved, and Reuters/Ipsos found that 33 percent approved while 56 percent disapproved. Although Trump usually has overwhelming backing from Republicans on most job approval questions, there were some signs that at least a few GOP voters were breaking with him on this issue. The CBS News/YouGov survey found that 65 percent approved of how he’s handling the situation — far lower than the 84 percent who approve of how he’s handling the coronavirus pandemic, for example — while 14 percent disapproved. Similarly, in the Reuters/Ipsos poll, 20 percent disapproved while 67 percent approved.
So it's clear (from the polling average) that people approve of Trump less overall, and it's clear (from these polls) that more people disapprove of his overall handling of the situation than approve of it. So it's reasonable to say that his handling of this situation is dragging down his overall average. But it's much harder to tie it to any specific event.
The closest you can come is to compare the dates that the polls were conducted to the news of the day. The Bible photo-op happened on June 1st, and to a rough eyeballing of the individual poll numbers from the list that drives the chart seems to indicate that the polls conducted after June 1st are notably worse for Trump than the ones before it.