The trick is using moisturizers with ceramides and hyaluronic acid, but in very light textures like serums or gel-creams, not thick creams. The thing is, seborrheic dermatitis is tricky because your skin barrier is damaged, so you need to repair it without overloading your skin with oils that'll feed the inflammation. I've been testing different products for a while now, and what really changed the game for me was switching from looking for "moisturizers for sensitive skin" to specifically looking for "barrier repair" formulas made with ceramides in decent proportions.
The order of application matters too. I apply the serum or moisturizer when my skin is still a bit damp after cleansing, because it helps it absorb better and doesn't end up feeling sticky. And then, if needed, a thin layer of a very light oil like jojoba or rosehip, but honestly just a minimal amount. Some days I don't even need it because the moisturizer alone is enough.
About the irritation thing: if it itches or dries out even with "safe" products, you're probably using too much or your skin is really inflamed at that moment. That's where it helps to start with tiny amounts and gradually increase. And if you can, once a week apply a slightly more generous layer before bed, like it's a night treatment, because your skin repairs itself better at night.