I agree. We use regular bleach in our HE washer all the time we it no issues.When it comes to bleach HE is a marketing ploy, all bleach is HE compatible.
As long as it is scentless and not splashless then it is just fine.
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Most Walmarts have a pool section near the outdoor area and sell HTH Liquid Chlorine @10% for two gallons for $6.50 to $7, better value than most laundry bleach