Neither freedoms nor liberties (nor, for that matter, rights) is appropriate here. These terms, without qualification, will be understood to designate political or legal liberties, which is exactly what you deny is at issue: "not because they are not allowed to".
The term we usually employ for access to the means of exercising those liberties is opportunity.
There are, moreover, other problems with your sentence, both idiomatic and substantive:
I trust that what precedes this sentence explains exactly what you mean by social inequality. But you should be aware that 'social inequality' usually designates a broader range of discriminants than just the economic and that the term usually includes precisely the matter of access to social goods which you seem to want to distinguish.
capabilities inequalities is not idiomatic. In the first place, it is rare for a plural to act as an attributive (see this discussion). More importantly, capability designates a person's internal capacity to perform some action, not the absence of external constraints, which is what you seem to be talking about.
The term stratification usually designates a series of discrete 'bands' rather than a continuous spectrum. Taken with the term categorized it seems to imply that what denies poor people the opportunities enjoyed by the affluent is not their actual poverty but the label which is put on them—which is something quite different from what is set forth in your explanation.
To be in deprivation of is not English. Use a passive instead— are deprived of. And consider whether are denied might be more appropriate: to 'deprive someone of X' is to take away the X which they have, to 'deny someone X' is to prevent them from obtaining it in the first place.