Terephthalohydrazide chitosan hydrogel (TCs) was prepared and investigated as an ecofriendly biopolymeric catalyst for synthesis of some novel thiazole and thiadiazole derivatives. Thus, TCs was used as a promising ecofriendly basic biocatalyst for preparation of three new series of thiazoles and two thiadiazoles derivatives via reacting 2-(2-oxo-1,2-diphenylethylidene) hydrazine-1-carbothio-amide with various hydrazonoyl chlorides and α-haloketones under mild ultrasonic irradiation. Also, their yield% was estimated using chitosan and TCs in a comparative study. The procedure being employed has the advantages of mild reaction conditions, quick reaction durations, and high reaction yields. It also benefits from the catalyst’s capacity to be reused several times without significantly losing potency. The chemical structures of the newly prepared compounds were confirmed by IR, MS, and 1H-NMR. Docking analyses of the synthesized compounds’ binding modes revealed promising binding scores against the various amino acids of the selected protein (PDB Code—1JIJ). SwissADME’s online tool is then used to analyze the physiochemical and pharmacokinetic characteristics of the most significant substances. The majority of novel compounds showed zero violation from Lipinski’s rule (Ro5).