The fermentation of fruit processing residuals (FPRs) with filamentous fungi can provide protein-rich food products. However, FPRs that contain bioactive compounds with antimicrobial properties present a major challenge. In this work, the resistance of two edible filamentous fungi, Rhizopus oligosporus and Neurospora intermedia, to 10 typically inhibiting bioactive compounds available in FPRs (epicatechin, quercetin, ellagic acid, betanin, octanol, hexanal, D-limonene, myrcene, car-3-ene, and ascorbic acid) was examined. These compounds’ inhibitory and stimulatory effects on fungal growth were examined individually. Three different concentrations (2.4, 24, and 240 mg/L) within the natural concentration range of these compounds in FPRs were tested. These bioactive compounds stimulated the growth yield and glucose consumption rate of R. oligosporus, while there was no increase in the biomass yield of N. intermedia. Ellagic acid caused an up to four-fold increase in the biomass yield of R. oligosporus. In addition, octanol and D-limonene showed antifungal effects against N. intermedia. These results may be helpful in the development of fungus-based novel fermented foods.