The large-scale environment of the cosmic web is believed to impact galaxy evolution, but there is still no consensus regarding the mechanisms. We use a semi-analytic model (SAM) galaxy catalog to study the star formation and dust content of local galaxies in different cosmic environments of the cosmic web—namely voids, filaments, walls, and nodes. We find a strong impact of the environment only for galaxies with M
stars ≲ 1010.8
M
⊙: the less dense the environment, the larger the star formation rate and dust content at fixed stellar mass. This is attributed to the fact that galaxies in less dense environments typically feature younger stellar populations, a slower evolution of their stellar mass, and delayed star formation compared to galaxies in denser environments. As for galaxies with M
stars ≳ 1010.8
M
⊙, the differences among environments are milder, due to the disk-instability-driven supermassive black hole (SMBH) growth implemented in the SAM, which makes SMBH growth, and thus galaxy quenching, environment-insensitive. We qualitatively test our predictions against observations by identifying environments in Sloan Digital Sky Survey Data Release 16 using dust masses derived from the GAMA survey. The agreement is encouraging, particularly at
log
M
stars
/
M
⊙
≳
10.5
–
11
, where the specific star formation rates and dust masses appear quite environment-insensitive. This result confirms the importance of in situ growth channels of SMBHs.