"Judging by growing social inequalities" or "Judging by the growing social inequalities" is fine. But "not so" doesn't sound quite right. (Difficult to suggest anything without more context; maybe "its nothing of the kind")
If I say "growing social inequalities in France and Anglo-Saxon countries", must I write "the" ?
Well, I think it works in the context but maybe I'm wrong. It's about the efficiency oh philanthropy and compulsory solidarity.
I wouldn't attempt to formulate a rule, but it seems to me that your original sentence sounds better with "the" because you are referring to a particular instance of growing social inequalities, namely that observed in France and Anglo Saxon countries. But it is not essential.
On your second question, "growing social inequalities in France and Anglo-Saxon countries" could be, among other things, the subject of a sentence:
"Growing social inequalities in France and Anglo-Saxon countries will probably result in social unrest"
which sounds fine.
Whether or not you use "the" may be a question of emphasis or it may simply be one of style.