It is enabled. I see no plugins that would be in conflict.

Here: https://www.dropbox.com/s/hcfxo76tbhay5qv/IMG_8A415FD8858A-1.jpeg?dl=0

Look at the rendered text. Its something like Times new roman. The code shows it correctly but its not on the front it. Look at the fonts on desktop (correct) and mobile (incorrect) side by side

Yes I did. I tried overriding them there. All are set on the mobile template for the element to either Playfair Display or Source Sans Pro, neither of which are rendering

This doesn’t work as you describe. Yes the category changes templates. But again, I’m asking for the Post to be rendered in a different template by category. Again:
\Category 1\ = Post uses Post Template A
\Category 2\ = Post uses Post Template B

I’m not understanding your response. My site is places.travel

Its not though. Here’s my header. I’ve clicked every column, row etc and no BG image
https://www.dropbox.com/transfer/AAAAAFlgHIc_8SgsrS1ML5MXeLMjd7t2vti-XvFL96jhDC_dVcW_5z0

Ditto, I can’t delete items.