Glide symmetry offers new degrees of freedom to engineer the properties of periodic structures, and thus it has been exploited in various electromagnetic structures. However, so far there has been little exploration on the impact that glide symmetry can offer in the field of acoustics. In this paper, we explore glide-symmetric acoustic waveguides, highlighting their dispersion characteristics and guiding properties and demonstrating opportunities in the context of acoustic devices. Here we analytically derive their dispersive features applying a semi-analytical mode matching technique. We then demonstrate how the unusual dispersion properties of glide-symmetric acoustic waveguides can be used to achieve very sharp frequency responses. Based on these results, we propose a sensing platform for liquid analytes that exhibits large sensitivity and linearity. Furthermore, by introducing fluid motion, we leverage these responses to design an acoustic isolator based on acoustic Mach-Zehnder interferometry, whose design is more favorable in terms of footprint and complexity in comparison to other acoustic nonreciprocal devices that do not rely on glide symmetry.