The stability of microgrid (MG) is affected by the interaction between parallel inverter-based resources (IBRs), especially when grid-forming (GFM) control is implemented in islanded MG to provide voltage support. In this paper, the robust stability analysis using structured singular value (SSV) approach and design of parallel GFM converters in islanded MG by structured μ synthesis are presented, catering to its multi-input multi-output (MIMO) nature. Specifically, a modular state-space model of parallel GFM converters in islanded MG is derived with component connection method (CCM). Model uncertainty is captured against the nominal model, delivering a certain degree of robustness for stability analysis, in the face of potential parametric uncertainty and resonance effects induced by parallel GFM converters. Moreover, the effects of system parameters on robust stability are comprehensively analyzed, and a robust design is proposed for virtual impedance (VI) tuning. The accuracy of modelling and robust stability analysis, as well as the effectiveness of the robust design is validated in MATLAB/Simulink/PLECS and real-time digital simulator (RTDS).