There was traditionally no stratification of Judaism among Sfaradim. There’s no Haredi, Modern Orthodox, left, right, etc etc. The are all recent Ashkenazic inventions. In Spehardic culture everyone is part of the fold. There’s no “Mihutz lamahane moshavo” as it were. If you were very pious, great. If you didn’t keep Shabbat 100% you were still accepted.
It should be noted that covering one’s head is a concept discussed way back in the Gemara. It’s not a recent thing. Everyone agrees that covering one’s head is virtuous. But it’s omission doesn’t make someone irreligious.