For the message separated by two underscores, e.g. CATEGORY__SUBCATEGORY, you should be able to turn them off by adding lines in log.ini (create it if it doesn't exist).
You can turn an entire category off by specifying CATEGORY=off, or just a subcategory with CATEGORY__SUBCATEGORY=off.
e.g.
Code:
LAUNCHER=off
WORLD__INIT=off