one web sdk - two domains - one browser

You can enable 3rd party cookie support in your Web SDK which will write a demdex.com cookie that can be read from both domains. 
This 3rd party cookie though can be heavily limited in lifetime depending on the browser.

Are you having links from domain abc to xyz? In those cases you can let WebSDK attach the identity information to the links as query params.

https://experienceleague.adobe.com/en/docs/experience-platform/collection/js/commands/appendidentitytourl