Testing difference in means for two bimodal distributions?

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I have two bimodal distributions of data with two peaks (one around 0 and the other around 1). I have provided an example of one of the distributions. enter image description here Although their means and variances are different, they both have peaks around the same x-axis markers. How do I test for difference in means using statistically rigorous approaches? Can I still use a t-test even though the data is not normally distributed?