We present an analysis of 152 355 radio sources identified in the second data release of the LOFAR Two Metre Sky Survey (LoTSS-DR2) with Sloan Digital Sky Survey (SDSS) spectroscopic redshifts in the range $0.00 z 0.57$. Using Monte Carlo simulations, we determine the reliability of each source exhibiting an excess in radio luminosity relative to that predicted from their H $\alpha$ emission, and, for a subset of 124 023 sources we combine this measurement with a full BPT analysis. Using these two independent diagnostics, we determine the reliability of each source hosting a supermassive black hole of high or low Eddington-scaled accretion rate, and combine the measurements to determine the reliability of sources belonging to each of four physical classes of objects: star-forming galaxies (SFGs), radio-quiet active galactic nuclei (RQAGN), and high- or low-excitation radio galaxies (HERGs or emission-line LERGs). The result is a catalogue that enables user-defined samples of radio sources with a reliability threshold suited to their science goal, for example prioritizing purity or completeness. Here, we select high-confidence samples of radio sources (>90 per cent reliability) to report: 38 588 radio-excess AGNs in the LoTSS-DR2 sample (362 HERGs, and 12 648 emission-line LERGs), together with 38 729 SFGs, and 18 726 RQAGN. We validate these results through comparison to literature using independent emission-line measurements, and to widely adopted WISE photometric selection techniques. While our use of SDSS spectroscopy limits our current analysis to $\sim 4$ per cent of the LoTSS-DR2 catalogue, our method is directly applicable to data from the forthcoming WEAVE-LOFAR survey, which will obtain over a million spectra of 144 MHz selected sources.