hetfak

Well, this was exhausting.
The cause of the problem was a link

/etc/mime.types -> /etc/mime.types.new

instead of an actual file. I did that myself, because I found that my original /etc/mime.types file did not have a

text/css css

line, and I did want to be able to switch between the updated and original more elegantly. (Paranoia of keeping track of all changes…)
Once I made an actual /etc/mime.types file with the text/css css line appended, and I restarted the Apache web server with

httpd -k stop
httpd -k start

my pain went away. The

httpd -k restart

did not give me the same result, for some reason. Odd.