Sendmail fails complaining: create file maildrop Permission denied

When trying to use sendmail from a script, it fails with

postdrop: warning: mail_queue_enter: create file maildrop/690025.14220: Permission denied

Output from ls -la /var/spool/postfix looks like this which is identical to the output on another Mac with working sendmail:

total 0
drwxr-xr-x  16 root      wheel      544 24 Sep  2016 .
drwxr-xr-x   6 root      wheel      204 21 Okt  2016 ..
drwx------   2 _postfix  wheel       68  8 Jan 17:22 active
drwx------   2 _postfix  wheel       68 11 Feb  2017 bounce
drwx------   2 _postfix  wheel       68 24 Sep  2016 corrupt
drwx------  11 _postfix  wheel      374 11 Feb  2017 defer
drwx------  11 _postfix  wheel      374 11 Feb  2017 deferred
drwx------   2 _postfix  wheel       68 24 Sep  2016 flush
drwx------   2 _postfix  wheel       68 24 Sep  2016 hold
drwx------   2 _postfix  wheel       68  8 Jan 17:22 incoming
drwx-wx---   2 _postfix  _postdrop   68 12 Feb  2017 maildrop
drwxr-xr-x  10 root      wheel      340  8 Jan 17:22 pid
drwx------  26 _postfix  wheel      884  8 Jan 17:22 private
drwx--x---   7 _postfix  _postdrop  238  8 Jan 17:22 public
drwx------   2 _postfix  wheel       68 24 Sep  2016 saved
drwx------   2 _postfix  wheel       68 24 Sep  2016 trace

I've searched the net for solutions and tried them, but they don't seem to work.
sudo postfix check gives me these messages:

postfix: Postfix is running with backwards-compatible default settings
postfix: See http://www.postfix.org/COMPATIBILITY_README.html for details
postfix: To disable backwards compatibility use "postconf compatibility_level=2" and "postfix reload"
/usr/sbin/postconf: warning: /etc/postfix/main.cf: unused parameter: mydomain_fallback=localhost

The last line is repeated approx. 20 times.

sudo postfix set-permissions results in the same output, plus

chown: /usr/libexec/postfix: Operation not permitted

When I try sendmail with sudo (no idea if that should work), I get

postdrop: warning: unable to look up public/pickup: No such file or directory

Any ideas how to fix that?