There is a point worth to be stressed in support of your concern; in logic we say that an argument is valid when we have a relation between premises and conclusion called : logical consequence.
We say that a sentence A is logical consequence of a set Γ of sentences, and we write : Γ ⊨ A, precisely when it is not possible that all the sentences in Γ are true and A is false.
In a Proof by Contradiction, we assume the negation of A : ¬A, and derive a contradiction; this shows that it is not possible that all the sentences in Γ and ¬A are simultaneously true.
But this implies that in every "situation" where all of Γ's are true (we say : all of Γ's are satisfied), ¬A is false; by properties of truth, if ¬A is false, then A is true; thus, we have established the relation of logical consequnce.
Bute there is a particular circumstance: when all of Γ's are already contradictory (i.e.unsatisfiable).
In this case it is not possible to find a "situation" where all of Γ's are simultaneously true (i.e.satisfied).
You can think at your example with an additional premise "on top" of (1)-(3) : (E ∧ ¬E).
What happen in this case ?
Well, applying the above definition of logical consequence, we have that :
if there is no "situation" that satisfies every member of Γ, then for any sentence A, it is vacuously true that Γ ⊨ A.
Thus, in presence of a contradcitory set of premises, like (1)-(3) with the additional (E ∧ ¬E), it is still true that they implies (C v D), simply because they, being contradictory, impliers everything.