Where do the rectors of German universities come from? From Germany, largely, at least according to what I can make out. Of a total of 83 current rectors, 76 (85%) are German in origin. This is largely in proportion to the number of professors who are German, which according to this article is above 90%.
The idea to do this came from a Facebook post by Roberta D'Alessandro doing a similar thing for the Netherlands. This percentage is perhaps not hugely surprising in itself, but the overall low proportion of non-German professors did surprise me. I work in a department which currently has 11 professors, 5 of whom were not born in Germany.
Looking at the seven exceptions is interesting, too. Four of them are from Switzerland or Austria, where they would in all likelihood have spoken German from a very young age. The same may be true of Elizabeth Prommer, rector of the University of Rostock, who, although California-born, went to school in Bavaria. That leaves the president of the small private Constructor University in Bremen, Stanislav Protasov, who was born in Tashkent (then USSR), and the president of the Karlsruhe Institute of Technology, Jan S. Hesthaven, who is Danish. Neither of these are hugely prototypical German universities, and in the former case it's been suggested that being mates with the man who owns the university may have played a significant role.
My feeling is that there's little antipathy to foreigners in the German academic system per se, but at the same time it's structurally quite difficult to penetrate due to its various idiosyncratic properties that the locals treat as self-evident natural truths about the universe. Actually running the show without German as one's native language would be a real challenge.
A quick note on methodology: I started with this list of universities, looked up who the rector or president is on Google, and tried to find their Wikipedia article. If this existed and stated where they were born or what their nationality was, I used that. Otherwise I tried to find another source, and this ultimately ended up being successful in all cases, so I didn't have to make inferences based on names. Unmarked entries in the list below are German.
Baden-Württemberg:
Kerstin Krieglstein
Frauke Melchior
Stephan Dabbert
(Danish) Jan S. Hesthaven
Thomas Fetzer
Peter Middendorf
Karla Pollmann
Michael Weber
Bayern:
Sabine Doering-Manteuffel
Kai Fischbach
Stefan Leible
Gabriele Gien
Joachim Hornegger
Thomas F. Hofmann
Bernd Huber
(Austrian) Eva-Maria Kern
Ulrich Bartosch
Udo Hebel
Paul Pauli
Berlin:
Günter M. Ziegler
Julia von Blumenthal
Geraldine Rauch
Brandenburg:
Gesine Grande
Eduard Mühle
Oliver Günther
Bremen:
Jutta Günther
(USSR) Stanislav Protasov
Hamburg:
Jörg Müller-Lietzkow
Andreas Timm-Giel
Hauke Heekeren
Klaus B. Beckmann
Hessen:
Tanja Brühl
Enrico Schleiff
Katharina Lorenz
Ute Clement
Thomas Nauss
Mecklenburg-Vorpommern:
Katharina Riedel
(American) Elizabeth Prommer
Niedersachsen:
Angela Ittel
Sylvia Schattauer
Metin Tolan
Volker Epping
(Swiss) Denise Hilfiker-Kleiner
Klaus Osterrieder
May-Britt Kallenrode
(German-Swiss) Sascha Spoun
Ralph Bruder
Susanne Menzel-Riedl
Verena Pietzner
Nordrhein-Westfalen:
Ulrich Rüdiger
Angelika Epple
Martin Paul
Michael Hoch
Manfred Bayer
Barbara Albert
Anja Steinbeck
Stefan Stürmer
Joybrato Mukherjee
Ansgar Thiel
Johannes Wessels
Birgitt Riegraf
Stefanie Reese
Martin Butzlaff
Birgitta Wolff
Rheinland-Pfalz:
Malte Drescher
Stefan Wehner
Georg Krausch
Holger Mühlenkamp
(Austrian) Eva Martha Eckkrammer
Saarland:
Ludger Santen
Sachsen:
Gerd Strohmeier
Ursula Staudinger
Klaus-Dieter Barbknecht
Eva Inés Obergfell
Sachsen-Anhalt:
Claudia Becker
Jens Strackeljan
Schleswig-Holstein:
Christiane Hipp
Insa Theesfeld
Enno Hartmann
Thüringen:
Walter Bauer-Wabnegg
Kai-Uwe Sattler
Andreas Marx
(Austrian) Peter Benz