Consider the event that there is a + crossing from left to right in a box for the Ising model on the triangular lattice. We show that this event is noise sensitive under Glauber dynamics t \mapsto \sigma_t in the subcritical regime \beta<\beta_c. We rely on the non-spectral approach from our previous work [TV23]. An important aspect in this more general setup is the study of the pair (\sigma_0,\sigma_t) and in particular the establishment of properties such as finite-energy and spatial mixing.