If there were one. The closest thing is the Treaty of Lisbon, which in turn was an update on the Treaties of Maastricht and Rome.

However, the matter has been heard in the European Court of Justice in 2002, and the short version is "Community law does not preclude compulsory military service being reserved to men."

For more details, feel free to study the legal opinion behind the ruling: https://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CEL...

It probably could be challenged under the German constitution, but nobody knows if that would be successful. The draft for men is set up in the constitution, but there is also an explicit equality for men and women in there. In the past any challenge would almost certainly have been denied, but it's a different time now.

In practice, this draft is not a real draft yet. Nobody is actually drafted, so there are almost no practical consequences. If there was an actual draft, I'd expect to see a challenge to this.

Not sure about constitution, but it is clearly discrimination based on sex, which violates plenty of EU laws and regulations.

I wouldn't trust the European Union to be the one that will challenge that German mobilization register at all.

COVID-19 has proven that if anything, the European Union tends to spread national initiatives among other countries (and Germany is often a leader in EU).

In this specific case, the EU is more likely to be the type of organization that would think about how to create a unified permit

-> as they did with the EU Digital COVID certificate; some sort of "I am in the register of mobilization" / "have a temporary travel authorization".

So, EU might be an enemy that pretends to be your friend there.

Theoretically yes, practically no. The ECJ can order the revision of national laws, but the country in question is responsible for implementation, and can send plaintiffs on a multi-decade merry chase. Several countries have also taken the view that they can refuse changes to their constitutions. This stands on shaky ground legally, but there is no real enforcement mechanism anyway.

I wonder why it is so trendy to want that.

Yeah, the law is unjust but spare even this part of the population this unnecessary risk. It's not like they can't join if they want to but why put force on it? So everybody feels miserable? What's the point?

And yeah, ich habe treu und tapfer verteidigt...