Social icons not showing

I have added social icon links inside the theme header using the customizer.

The social icons display while editing the customizer but disappear after I publish and close the customizer – not showing up in the theme.

If I go back to the customizer the links are saved but the icons don’t show until I edit the links in some way (like deleting and re-adding characters). When I publish and close the customizer, they all disappear again.

The links are to Facebook, Twitter, YouTube and RSS feed. They are all correctly linking to pages that exist.

Does anyone have any idea why this is happening? What could I try to fix it?

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