We aim to better understand the emission of molecular tracers of the diffuse and dense gas in giant molecular clouds and the influence that metallicity, optical extinction, density, far-UV field, and star formation rate have on these tracers. Using the IRAM 30m telescope, we detected HCN, HCO+, 12CO, and 13CO in six GMCs along the major axis of M33 at a resolution of ~ 114pc and out to a radial distance of 3.4kpc. Optical, far-infrared, and submillimeter data from Herschel and other observatories complement these observations. To interpret the observed molecular line emission, we created two grids of models of photon-dominated regions, one for solar and one for M33-type subsolar metallicity. The observed HCO+/HCN line ratios range between 1.1 and 2.5. Similarly high ratios have been observed in the Large Magellanic Cloud. The HCN/CO ratio varies between 0.4% and 2.9% in the disk of M33. The 12CO/13CO line ratio varies between 9 and 15 similar to variations found in the diffuse gas and the centers of GMCs of the Milky Way. Stacking of all spectra allowed HNC and C2H to be detected. The resulting HCO+/HNC and HCN/HNC ratios of ~ 8 and 6, respectively, lie at the high end of ratios observed in a large set of (ultra-)luminous infrared galaxies. HCN abundances are lower in the subsolar metallicity PDR models, while HCO+ abundances are enhanced. For HCN this effect is more pronounced at low optical extinctions. The observed HCO+/HCN and HCN/CO line ratios are naturally explained by subsolar PDR models of low optical extinctions between 4 and 10 mag and of moderate densities of n = 3x10^3 - 3x10^4 cm^-3, while the FUV field strength only has a small effect on the modeled line ratios. The line ratios are almost equally well reproduced by the solar-metallicity models, indicating that variations in metallicity only play a minor role in influencing these line ratios.