A new approach to functionalize the surface of polyester textiles is described in this study. Functionalization was achieved by incorporating pH/temperature-responsive polyelectrolyte microgels into the textile surface layer using UV irradiation. The aim of functionalization was to regulate polyester wettability according to ambient conditions by imparting stimuli-responsiveness from the microgel to the textile itself. Microgels consisted of pH/thermo-responsive microparticles of poly(N-isopropylacrylamide-co-acrylic acid) either alone or complexed with the pH-responsive natural polysaccharide chitosan. Scanning Electron Microscopy, X-ray Photoelectron Spectroscopy, ζ-potential measurements, and topographical analysis were used for surface characterization. Wettability of polyester textiles was assessed by dynamic wetting, water vapor transfer, and moisture regain measurements. One of the main findings showed that the polyester surface was rendered pH-responsive, both in acidic and alkaline pH region, owing to the microgel incorporation. With a marked relaxation in their structure and an increase in their microporosity, the functionalized textiles exhibited higher water vapor transfer rates both at 20 and 40 °C, and 65% relative humidity compared with the reference polyester. Also, at 40 °C, i.e., above the microgel Lower Critical Solution Temperature, the functionalized polyester textiles had lower moisture regains than the reference. Finally, the type of the incorporated microgel affected significantly the polyester total absorption times, with an up to 300% increase in one case and an up to 80% decrease in another case. These findings are promising for the development of functional textile materials with possible applications in biotechnology, technical, and protective clothing.