Egypt has no beef with Palestine, but the military regime running it has been more interested in Western aid and loans than having anything resembling sovereignty since the 80s. This became much worse in 2014 after they retook power, with Western money pretty much the only thing standing between the regime and total collapse due to rampant corruption and mismanagement preventing anything resembling a healthy economy from developing. My best guess for this particular farce is that if Egypt allowed these people in only to turn them away at Rafah after they get local media attention, it’d expose Egypt’s role as an enforcer of Israeli will to the Egyptian public (which they for the most part aren’t aware of). Egypt also has China-level political repression, so the government really doesn’t tolerate independent political action.

Source: Am Egyptian, please someone nuke us already.

TL;DR: Money. Egypt is a paid enforcer for Israel.

Edit: I’m also glossing over Iran foreign policy aspects of this, but really it’s the money.