The most likely cause for your flare up, assuming that it’s water related is under rinsed clothing and linens after washing.
Softened water requires much less detergent so reduce your use per wash by at least 50%.
Keep in mind the usage advice on the packaging is written by someone who sells detergent.
Also existing fabrics that have been regularly washed in hard water will have soap residue in them.
Rinsing and spinning bedding in softened water without washing frequently gives a lather just from the soap residue.
Another possibility is some water softeners do not include a fast rinse or backwash cycle in the regeneration process.
This can leave residual sodium salts in the water immediately after regeneration.
Which water softener are you using?