Is any term within a quantum lagrangian equal to its transpose?

A lagrangian is a scalar under any relevant symmetry group (at least in standard theory). This would make me think that we can take any single term within any lagrangian and transpose it without repercussions -- doing any subsequent algebra correctly (taking fermionic anti-commutation into account, for instance), of course. Is this correct?

I'm not sure how the fact that the degrees of freedom here are operator-valued fields can mess with this conclusion -- even if the transposition regards only Lorentz spinor indices.

For instance, consider an interaction term of a doubly-charged vector boson with a pair of same-sign charged leptons. Can we 'impose' the first equality below

$$U^{++}\bar{\ell_b^c}\gamma_\mu P_L \ell_a=(U^{++}\bar{\ell_b^c}\gamma_\mu P_L \ell_a)^T=-U^{++}\bar{\ell_a^c}\gamma_\mu P_R\ell_b$$

(where $$\ell^c$$ is the charge conjugate of $$\ell$$ and the $$P$$ are chirality projectors)?