The main takeaway being put forward from the EU elections is a massive shift to the right and while that is true on paper if you scratch the surface it gets more complicated.
The right wing underperformed the polls in a number of countries and the left made gains in Scandanavia. Most of the rights advances came in France & Germany, which given their large populations & therefore seat allocation did most of the heavey lifting.
It would be wrong to view the right as some sort of homogeneous monolith where everyone votes for the same reason
In the data above we see that immigration is the number one issue across the continent but that only edges out cost of living which was a bigger factor for right wing voters than immigration in Spain, Poland & Italy.
The terms left & right are sort of bubble terms, people don't think to themselves what the left wing view of X or the right wing view of Y, they ask what they think & find the party accordingly and of course can have views that vary across the spectrum.
You can be fiscally conservative & socially liberal but vote for a socially conservative party because you prioritise economic security over same sex marriage.
This bears out when you look at the parties & their leaders, the commentariat like to group them altogether & they do have many similarities but Orban is a Christian Nationalist, his opposition to Islam & immigration is based on that. Dutch society however is aggresively secular, Wilders opposition to Islam & immigration is based on the preservation of that secularism & it is why Wilder & Orban have very different views when it comes to LGBT issues. Likewise Le Pen may be Eurosceptic & want to see a reduction of immigration & a curtailment of Islam but her economic platform at the last Presidential election was almost Corbynite, probably why she is so popular with young French voters
When looking at European elections whether domestic or EU wide they take place under a PR voting system so elections are more pluralistic and its easier for voters to move among the parties knowing their vote will still count as opposed to a fptp system in The UK & US, resulting in multiple parties with smaller vote shares and coalition governments.
As a result people who traditionally vote left & find themselves unhappy with the governmemt but can't vote for their traditional party, or any other left wing party, because they are part of a three or more party coalition, may only have the populist right party as as a means of showing their dissatisfaction
As mentioned earlier the results have been driven by France & Germany, both who have unpopular left wing Governments, its safe to assume that in those countries the elections were less about the EU and its direction & more as a referendum on the incumbent domestic administrations. Were Macron & Scholz enjoying strong poll ratings or the two countries had unpopular right wing governments the left would of had a good night on Sunday & the outcome at The EU level would look different