Alternating Grip W/ Deadlifts

I’ve been dead lifting for a while with straps and recently decided to stop using them. The only way I’m able to hang on, though is if I face my left palm out, right palm in. When I alternate to the other way around, I don’t feel as though I’m picking the weights up evenly and it affects my lift. Is it okay to just stick with one way of gripping the bar? Would I begin to develop significant imbalances?

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