Are interacting symmetry protected topological (SPT) phases and symmetry enriched topological (SET) phases must be gapped?

I wonder are interacting SPT and SET phases gaped? Can we have a SET or interacting SPT phase in a semi metal?

As usual, the dots indicate Majorana operators $$c_j$$ and the bonds are pairing terms $$ic_1 c_2$$ so that you can read each picture as a Hamiltonian.
Consider placing a chain with Hamiltonian $$H_1$$ (the Kitaev wire) on top of one with $$H_0 + H_1$$ (massless free Majorana field, a 1d semimetal). Then it's possible to absorb the edge modes of $$H_1$$ into those of $$H_0 + H_1$$ with a local term.