Example: There is a group of customers who “are of” a similar age, the same sex.
Does it mean “belong to”, and what else does it possibly mean in other contexts?
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The short answer is yes. The phrase “be of” means to belong to something, or identify with something, like a demographic or a requirement. Your first example is one of the most common phrases where “be of” is used, to be of age. In this case, it doesn't exactly mean “belong to”, but it means that you have enough age, rather than meaning that you have age. The word have doesn't always work, though. Your second example illustrates this, with being of the same sex, which can be misinterpreted if “have” is used. The OED uses an example, which doesn't use exactly the same interpretation, but still can be translated roughly to have.
‘this work is of great interest and value’
Some other examples from the OED illustrate your uses better:
‘The school has a number of buildings listed as being of historic interest.’