Does swearing a civil-servant oath to uphold the Constitution and laws in countries like Luxembourg, whose laws conflict with Sharia (inheritance, religious freedom), constitute shirk or kufr under Quran 5:44? Does it differ if one complies administratively for work, not out of conviction?

Kufr in this ayah is for the one who holds ruling by other than what Allah revealed to be permissible, equal to it, or better, as Shaykh Ibn Baz and Shaykh Ibn Uthaymin and the Imams before them have explained. As for making such oaths, then try to find a way out by explaining to them your situation and for example making an Islamic oath to carry out justice etc. Otherwise, you can try to avoid it if possible or find other work also if possible.