Answer
Are journals with no publication fee lower quality?
No. Journals without author charges are usually funded by a university, learned society, ministry or consortium rather than by authors. Author-pays became the default in commercial publishing, not in scholarly publishing as a whole, and many no-fee titles sit in the first quartile of their fields.
Detail
Two different things get called 'no fee'
Diamond journals are free to read and free to publish in. Subscription journals also charge authors nothing, but readers pay, and some funders will not accept that route.