The increased use of bioplastics in the market has led to their presence in municipal solid waste streams alongside traditional fossil-based polymers, particularly low-density polyethylene (LDPE), which bioplastics often end up mixed with. This study aimed to assess the impact of cellulose acetate plasticized with triacetin (CAT) on the mechanical recycling of LDPE. LDPE–CAT blends with varying CAT content (0%, 1%, 5%, 7.5%, and 10% by weight) were prepared by melt extrusion and analyzed using scanning electron microscopy, Fourier-transform infrared spectroscopy, thermal analysis (thermogravimetric and differential scanning calorimetry), dynamic rheological measurements, and tensile tests. The results indicate that the presence of CAT does not significantly affect the chemical, thermal, and rheological properties of LDPE, and the addition of CAT at different levels does not promote LDPE degradation under typical processing conditions. However, the addition of CAT negatively impacts the processability and mechanical behavior of LDPE, resulting in the reduced quality of the recycled material. Thus, the presence of cellulose-based bioplastics in LDPE recycling streams should be avoided, and a specific sorting stream for bioplastics should be established.