On Tuesday, new Members of the European Parliament (MEPs) took their seats for the first time since a dramatic set of elections in May shook up the status quo.

As the new-look parliament stood for the iconic melody from Beethoven's ninth symphony, commonly known as Ode to Joy and the unofficial anthem of Europe, MEPs from the UK's Brexit Party turned their backs in protest.

Europhiles called the protest disrespectful. "What's disrespectful is to take the ancient nations states of Europe and, without asking anyone, turn them into a country," said Nigel Farage, the Brexit Party's leader.

You might think that opinions of a political party named after a movement to leave the European Union shouldn't matter much to EU officials. But Farage's group is the largest single party in the European Parliament. And it's not just Euroskeptics that are making life difficult for supporters of the European project at the moment.

As Europe's voters become increasingly hostile to business-as-usual politics, EU leaders tried to pull off an almighty stitch-up and force establishment figures into the bloc's four top jobs -- including the most powerful job in Brussels, president of the European Commission.

After three days of horse trading, the German defense minister Ursula von der Leyen was lined up to take this post. Her nomination -- which came out of the blue -- is a near-perfect illustration of the problems facing a Europe rocked by populism and a general distrust of the establishment.

Here's how the process works. The commission president is decided in two stages: First, the leaders of the 28 EU member states must agree on a name. That person must then be approved by a simple majority of the the 751 members of the European Parliament.

Ordinarily, that process is a formality. But May's EU elections were a clear indication of the mixed feelings across the continent in 2019. Establishment parties lost seats to both Euroskeptic parties, like the Brexit party and the Italian far-right Leage, and pro-EU reform parties, like the German Greens and French President Macron's En Marche movement.

This has severely compromised the old coalition between the center-right and center-left groups to get what they want in Brussels and freeze out everyone else.

In turn, this means that the only way to get someone everyone can agree on is to pluck bland "compromise" candidates who have little baggage.

But there is a fine line between a compromise in which all parties accept they don't get exactly what they want and ending up with a situation that everyone hates.

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Here we come back to the Leyen nomination. The majority of the center-left bloc in parliament is livid that their first choice, the Dutch Labour politician Franz Timmermans, was so quickly swept aside by the 28 EU leaders. He was not the only qualified candidate to be brushed off: The candidacy of the former favorite, Germany's Manfred Weber, also fell apart. Eastern European nations, such as Hungary, could not stomach a candidate with a track record of standing up to the nationalist leaders who typically run these countries.

Charitably, Leyen is seen as an unusual choice. Less charitably, she could be described as a very small fish on the European stage. She has a patchy record as Germany's defense minster and critics say she has no real history in the pan-European policy arena.

That would suit strongmen leaders in the east for obvious reasons. But it also suits French President Emmanuel Macron. One of Leyen's only publicly-known European policies is her support of a European army, something Macron badly wants to lead the charge on. Her perceived weakness on European politics also allows Macron to take a larger role on the European stage, an opportunity he has been keen to grasp as his popularity in France fluctuates.

And by getting behind the Leyen nomination, Macron is seen to be supporting the idea of a German in the top job without that German being Weber, whom Macron might anticipate as being harder to "help" find his feet in the job.

Of course, this might backfire for Macron and other supporters of Leyen. Some think their perception of her as weak could be rooted in misogyny. And German diplomats say that she is a formidable character and that while her record in post is not wholly positive, she is tough and not likely to be pushed around.

That's if she makes it into the job at all. The center-left Socialists and Democrats (S&D) in the European Parliament are trying to convince MEPs that the appointment would be illegitimate, as it goes against a resolution passed in May which says that only someone previously declared as being interested in the top job can become the next commission president. Ignore that, and what is the point of parliament?

But even the S&D group is divided. The EU makes top appointments as part of a package deal, designed to give everyone all countries a little of what they want. That's how Christine Lagarde, the boss of the International Monetary Fund, ended up being put forward for president of the European Central Bank , despite not having previously been linked to the role.

One of the more perplexing nominations was that of Spain's Josep Borrell for the top foreign affairs job. The idea was that by handing the top job to a Spaniard, it might persuade MEPs to approve the package as a whole. But it's on a knife edge and some observers wonder whether, if the deal goes down really badly, a new slate of appointees could be required -- perhaps sooner, rather than later.

So it's all a bit of a mess. In all probability, this will be resolved quickly as European politicians are on the whole pragmatic. But this is just step one. The reality facing whoever takes these jobs is that the 28 members of the European Union are becoming increasingly polarized. Hiring for the top jobs in European politics is seldom without its difficulties, given the money and power involved. But on the whole, this should be the easy bit.

As populists and anti-establishment parties dig their heels in over the next five years, things are not about to get any easier for the European institutions that embody everything so many on the continent despise.