satisfiability – Is the following problem NP-Complete?

No. This problem is equivalent to XOR-3SAT, in which we interpret each clause as $x oplus y oplus z$, where $oplus$ is the XOR operator, and ask whether it’s possible to find values for all variables so that each clause is true. XOR-SAT can be solved in polynomial time using Gaussian elimination, with all arithmetic done modulo 2 (i.e., in the finite field $GF(2)$).