This can have an effect in exactly two ways:
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retailers lose a bit of profit because they cannot optimize their staffing for this one day. They might be a little less profitable because they have one person at work who is not needed, for example. They might also get mad customers the next day when everybody goes back shopping and they haven't prepared for it. Similarly, they might have to throw away a few fresh products and not have them in stock later.
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if (and only if) people buy the stuff they need somewhere else instead. If this is about grocery shopping, well, you need groceries at some point. Doesn't matter much for the retailer when you buy it (apart from 1), as long as you buy it consistently at their place.
I support the protest, but if you want to make an impact, use that day to find alternative places to do your shopping in the future.