Turbulence is a crucial flow phenomenon for tidal energy converters (TECs), as it influences both the peak loads they experience and their fatigue life. To best mitigate its effects we must understand both turbulence itself and how it induces loads on TECs. To that end, this paper presents the results of blade element momentum theory (BEMT) simulations of flume-scale TEC models subjected to synthetic turbulent flows. Synthetic turbulence methods produce three-dimensional flowfields from limited data, without solving the equations governing fluid motion. These flowfields are non-physical, but match key statistical properties of real turbulence and are much quicker and computationally cheaper to produce. This study employs two synthetic turbulence generation methods: the synthetic eddy method and the spectral Sandia method. The response of the TECs to the synthetic turbulence is predicted using a robust BEMT model, modified from the classical formulation of BEMT. We show that, for the cases investigated, TEC load variability is lower in stall operation than at higher tip speed ratios. The variability of turbine loads has a straightforward relationship to the turbulence intensity of the inflow. Spectral properties of the velocity field are not fully reflected in the spectra of TEC loads.