Metasurface-empowered bound state in the continuum (BIC) provides a unique route for fascinating functional devices with infinitely high quality factors. This method is particularly attractive to the terahertz community because it may essentially solve the deficiencies in terahertz filters, sensors, lasers, and nonlinear sources. However, most BIC metasurfaces are limited to specified incident angles that seriously dim their application prospects. Here, we propose that a dual-period dielectric metagrating can support multiple families of BICs that originate from guided mode resonances in the dielectric grating and exhibit infinite quality factors at arbitrarily tilted incidence. This robustness was analyzed based on the Bloch theory and verified at tilted incident angles. We also demonstrate that inducing geometric asymmetry is an efficient way to manipulate the leakage and coupling of these BICs, which can mimic the electromagnetically induced transparency (EIT) effect in our dual-period metagrating. In this demonstration, a slow-light effect with a measured group delay of 117 ps was achieved. The incidence-insensitive BICs proposed here may greatly extend the application scenarios of the BIC effect. The high Q factor and outstanding slow-light effect in the metagrating show exciting prospects in realizing high-performance filters, sensors, and modulators for prompting terahertz applications.