We investigate by time-resolved Synchrotron ultra-small X-ray scattering the dynamics of liquid-liquid phase-separation (LLPS) of gluten protein suspensions following a temperature quench. Samples at a fixed concentration (237 mg/ml) but with different protein compositions are investigated. In our experimental conditions, we show that fluid viscoelastic samples depleted in polymeric glutenin phase-separate following a spinodal decomposition process. We quantitatively probe the late stage coarsening that results from a competition between thermodynamics that speeds up the coarsening rate as the quench depth increases, and transport that slows downs the rate. For even deeper quenches, the even higher viscoelasticity of the continuous phase leads to a "quasi" arrested phase separation. Anomalous phase-separation dynamics is by contrast measured for a gel sample rich in glutenin, due to elastic constraints. This work illustrates the role of viscoelasticity in the dynamics of LLPS in protein dispersions.