Think of self starvation protests, but at an organizational level.
An (IMO equally valid) way of looking at it is that the EU is not 'the enemy' but rather someone you hoped was your ally. But now they're acting against your mission, in a way you feel is unacceptable. They've changed and you can no longer stand with them. In that situation, disassociating from them (with no regard for the tactics) is a sign of integrity.
Altough one could critize the way refugees we're handled by the authorities - instead of mixing them with the population and surfacing all kinds of tensions, they should have closed, but safe and decent refugee camps, and seperate refugees from the population(and also solve the issue of economic immigration). but now might be too late.
> and also solve the issue of economic immigration
Yeah, like that was easy :) most immigrants actually come from failed states like Eritrea, which you just can't "fix" in any easy way. I do agree that economic migrants should be treated differently from war refugees; as in, we should find ways to power economic and social programs that would directly allow economic migrants to return. Pay them to dig holes over there, if necessary. It won't fix the country, but it should stem the flow.
War refugees should be hosted and treated humanly though. Their conflicts are often "our" direct fault and we have an obligation to treat them fairly. US/UK/France are particularly bad in this, constantly getting involved in all sorts of international diatribes while rarely (if ever) actually picking up the tab when things go to hell.
To be fair, US got dragged into open conflict in ME and surrounding region because Saddam invaded Saudi. And Afg because of 9/11.
There are other nations that cause troubles outside of their border and don't pick up the tab when things go bad.
-China in Korean War, helping North Korea survive.
-Japan and Korean peninsula. Japan's colonization of Korea in 1910 ultimately led to creation of the monster called North Korea.
-Indonesian invasion of East Timor
-Germany stopped causing trouble internationally only after the entire nation was put under foreign occupation for decades after WW2.
Pretty much any nation is capable of causing trouble internationally. Most just can't do it at the scale of US/UK/France, because they don't have the ability, not because they are somehow better members of international community.
Refugees in the EU would not need Doctors Without Borders; in Turkey, refugees will need Doctors Without Borders.
If the EU wants to help Doctors Without Borders' mission, then it needs to take refugees and help them, not make more refugees Doctors Without Borders to help.
Let's say the EU is your enemy. They offer you money. Is it tactically smarter to flatly refuse the money (you are poorer, your enemy is marginally richer, nothing has changed) or rather to accept the money and then use it to fight the donor (you are richer, your enemy is marginally poorer and you are effectively turning its resources against itself)?
It feels a lot like cutting your own nose to spite the wife.