The crossed molecular beam reactions of ground state methylidyne, CH(X²Π), with D2-acetylene, C₂D₂(X¹Σ_g⁺), and of D1-methylidyne, CD(X²Π), with acetylene, C₂H₂(X¹Σ_g⁺), were conducted under single collision conditions at a collision energy of 17 kJ mol⁻¹. Four competing reaction channels were identified in each system following atomic ‘hydrogen’ (H/D) and molecular ‘hydrogen’ (H₂/D₂/HD) losses. The reaction dynamics were found to be indirect via complex formation and were initiated by two barrierless-addition pathways of methylidyne/D1-methylidyne to one and to both carbon atoms of the D2-acetylene/acetylene reactant yielding HCCDCD/DCCHCH and c-C₃D₂H/c-C₃H₂D collision complexes, respectively. The latter decomposed via atomic hydrogen/deuterium ejection to form the thermodynamically most stable cyclopropenylidene species (c-C₃H₂, c-C₃D₂, c-C₃DH). On the other hand, the HCCDCD/DCCHCH adducts underwent hydrogen/deuterium shifts to form the propargyl radicals (HDCCCD, D₂CCCH; HDCCCH, H₂CCCD) followed by molecular ‘hydrogen’ losses within the rotational plane of the decomposing complex yielding l-C₃H/l-C₃D. Quantitatively, our crossed beam studies suggest a dominating atomic compared to molecular ‘hydrogen’ loss with fractions of 81 ± 23% vs. 19 ± 10% for the CD/C₂H₂ and 87 ± 30% vs. 13 ± 4% for the CH/C₂D₂ systems. The role of these reactions in the formation of interstellar isomers of C₃H₂ and C₃H is also discussed.