Ultrasound imaging of the tongue is biased by the probe movements relative to the speaker's head. Two common remedies are restricting or algorithmically compensating for such movements, each with its own challenges. We describe these challenges in details and evaluate an open-source, adjustable probe stabilizer for ultrasound (ALPHUS), specifically designed to address these challenges by restricting uncorrectable probe movements while allowing for correctable ones (e.g., jaw opening) to facilitate naturalness. The stabilizer is highly modular and adaptable to different users (e.g., adults and children) and different research/clinical needs (e.g., imaging in both midsagittal and coronal orientations). The results of three experiments show that probe movement over uncorrectable degrees of freedom was negligible, while movement over correctable degrees of freedom that could be compensated through post-processing alignment was relatively large, indicating unconstrained articulation over parameters relevant for natural speech. Results also showed that probe movements as small as 5 mm or 2 degrees can neutralize phonemic contrasts in ultrasound tongue positions. This demonstrates that while stabilized but uncorrected ultrasound imaging can provide reliable tongue shape information (e.g., curvature or complexity), accurate tongue position (e.g., height or backness) with respect to vocal tract hard structure needs correction for probe displacement relative to the head.