I've just gone through the Remix deployment guide on pages and successfully deployed a very simple app. It built fine and is accessible via the .page.dev hostname.
I then went to add a custom domain. thorpevillage.com is hosted by Cloudflare, so I added wwwtest.thorpevillage.com. Looking at the domain I can see that Cloudflare has automatically created a CNAME record that is proxied through Cloudflare and is pointing correctly to www-thorpevillage-com.pages.dev.
However when I visit that URL, I get a Cloudflare error page (attached). If I look at the custom domain in my pages project, it shows as "Inactive (error)".