Evanescently coupled waveguide arrays provide a tabletop platform to realize a variety of Hamiltonians, where physical waveguides correspond to the individual sites of a tight-binding lattice. Nontrivial spatial structure of the waveguide modes enriches this picture and uncovers further possibilities. Here, we demonstrate that the effective coupling between p-like modes of adjacent photonic waveguides changes its sign depending on their relative orientation vanishing for proper alignment at a so-called invisibility angle. Using femtosecond laser-written waveguides, we demonstrate this experimentally for p-mode dimers and graphene-like photonic lattices exhibiting quasi-flat bands at this angle. We observe diffraction-free propagation of corner and bulk states, providing robust experimental evidence of a two-dimensional Aharonov-Bohm-like caging in an optically switchable system.