I want to express in a formula that variables with a certain property shall be added. I think it is best expressed by an example.
$A$ is a superset of $B$ and $C$.
$B$ can have the properties $X$ and $Y$.
$C$ also can have the properties $X$ and $Y$.
I want to sum up all $B$'s and $C$'s with the property $X$.
Is it correct to write
$$ \sum_{x\in A}( B_x + C_x ) ?$$
No, that notation does not do what it sounds like you want. If I understand you correctly, you mean
$A$ is a superset of both $B$ and $C$.
An element of $B$ may or may not have the property $X$.
An element of $C$ may or may not have the property $X$.
You want to sum all the elements of $B$ and $C$ that have the property $X$.
I would write something like
$$ \sum_{s\in B\cup C, X(s)} s $$
or
$$ \sum_{s\in (B\cup C)\cap X} s $$
depending on how you prefer to write down "has the property X" symbolically.
