The discovery of the M-{sigma} relation, the local galaxy bimodality, and the link between black-hole and host-galaxy properties have raised the question of whether active galactic nuclei (AGN) play a role in galaxy evolution. AGN feedback is one of the biggest observational challenges of modern extragalactic astrophysics. Several theoretical models implement AGN feedback to explain the observed galaxy luminosity function and, possibly, the color and morphological transformation of spiral galaxies into passive ellipticals. For understanding the importance of AGN feedback, a study of the AGN populations in the radio-optical domain is crucial. A mass sequence linking star-forming galaxies and AGN has already been noted in previous works, and it is now investigated as a possible evolutionary sequence. We observed a sample of 119 intermediate-redshift (0.04<=z<0.4) SDSS-FIRST radio emitters with the Effelsberg 100-m telescope at 4.85 and 10.45GHz and obtained spectral indices. The sample includes star-forming galaxies, composite galaxies (with mixed contribution to line emission from star formation and AGN activity), Seyferts, and low ionization narrow emission region (LINER) galaxies. With these sources we search for possible evidence of spectral evolution and a link between optical and radio emission in intermediate-redshift galaxies. We find indications of spectral index flattening in high-metallicity star-forming galaxies, composite galaxies, and Seyferts. This "flattening sequence" along the [NII]-based emission-line diagnostic diagram is consistent with the hardening of galaxy ionizing field, thanks to nuclear activity. After combining our data with FIRST measurements at 1.4GHz, we find that the three-point radio spectra of Seyferts and LINERs show substantial differences, which are attributable to small radio core components and larger (arcsecond sized) jet/lobe components, respectively. A visual inspection of FIRST images seems to confirm this hypothesis. Galaxies along this sequence are hypothesized to be transitioning from the active star-forming galaxies (blue cloud) to the passive elliptical galaxies (red sequence). This supports the suggestion that AGN both play a role in shutting down star formation and allow the transition from one galaxy class to the other.