There's another reason: People actually went to vote.
Low turnout always favors the more extreme parties, as their supporters go and vote either way. On a low turnout, that makes a big part of the total votes. However, when the turnout is high, they get overshadowed by the mass of votes to the other parties, making their share of votes pretty small in the end.
That's actually untrue. Most data-points shows that high turnout usually correlates with bad results for governing or big parties. It is explainable: if people are fine with things are going, they aren't seeing a reason to vote, as things can go on as they are. If people want to change things, they go vote. And the party or parties in power are not seen as a beacon of change. This is true for this election, the two biggest blocs european peoples party (EPP, conservatives) and S&D (social democrats) lost massively. Both lost more than 30 seats, they no longer have a majority together.
It is also untrue that extremists have a stable voterbase. If you look at the actual absolute votes they get, it fluctuates a lot. This makes sense too: if your goal is to fight or end democracy it doesn't make too much sense to participate in democratic process.
This doesn't mean that with high turnout each of the smaller parties get to profit in the same way. It strongly depends which topic activates you out of non-voting. Here in germany a strong activating topic was climate change, and what do you see: the greens doubled their result from 10% to over 20%. In other countries you have different topics that activate the people. So the result differs, in some you have wins for the rights, in some for the liberals.