Unless you're working in an English-speaking country, speaking English on the workfloor is actually quite tiring. Speaking a second language requires more thought and more deliberate speech to get the message across. I can understand why people coming from another country, who likely already need to speak their second language all day anyway, might not realise this, as this is "normal" for them anyway.
I work within a team of mostly Dutch people, with a few Eastern European/West Asian people. We try to stick to English, at least when our foreign coworkers are around, but everyone automatically switches back to Dutch every now and then. Some of the Bulgarian people in our team do the same when they're talking amongst themselves and I can't blame them!
I've only started noticing the mental impact of speaking a second language all day when there were days that there were only Dutch speaking people in the office. At the end of the day, I didn't feel as tired as during the "English speaking" days, even though I feel my English is good enough to express myself most of the time. This makes me think there's a subconscious toll in working with internationals that might not be apparent to some.
However, having a meeting with someone who doesn't speak the local language and not even trying to stick to English is just plain rude and unprofessional in my opinion. I can understand someone making a quick comment to a colleague, but switching between languages to have an actual discussion is just rude.
It sounds to me like the goals of the company and the goals of the individual teams don't align. The teams seem to want to talk in their native language, but the company seems to want to attract international workers.
In the end, productivity of the team is based on how well people work together. People from similar backgrounds, with similar experiences, tend to have fewer hurdles to get through. A team of ethnically diverse people, sharing the experience of moving to another country and culture, might have more in common as well; they might just work together better than if they were to be mixed homogeneously across the company.
I don't know what people apply to jobs in your company so I can't say if they're being discriminatory or not. Maybe the "diversity hiring manager" likes to accept inferior applicants to fill some diversity quotum; maybe the other ones are actually discriminating against applicants. If you think they're actively discriminating against foreign applicants, you should probably tell someone.
However, I wouldn't call preferring someone who speaks the local language fluently "illegal discrimination", although the distinction is often difficult to make. Just because official policy says that English is the language on the workfloor doesn't mean people will want to speak it all day. If you try to enforce a policy people don't seem to like, you'll probably only end up seeing the policy get changed.
Lastly: the EU may be somewhat culturally connected, but these issues will be different from country to country, region to region, and even city to city. There's a running joke on how the Germans won't speak anything but German, even during corporate meetings with other companies. I've heard stories of CEOs meeting with other companies where they spoke English and their German counterpart only answered in German, requiring someone who spoke both languages to translate for them, for example; this was such an alien concept to me that I laughed at the story, but I wouldn't ever want to work in such a situation!
There are just ways in which the Dutch do business differently from the Germans, the French, or the English, despite centuries of close trade and cultural exchange. I'm not saying this makes your situation right in any way, but you should know that your experience might not apply to the entire EU (or even the country you're in).