Just to update:
Based on ASDA’s confirmation, our graphs, and reports through in-app support chat, we believe that Monzo cards are now fully working at ASDA fuel stations again.
We still do not know exactly why this happened (and sadly, may never do) but after a lot of investigation and discussion, we do not believe it was intentional against Monzo.
More generally, it does look like pay at pump systems will be changing a lot over the next year with UK supermarket fuel stations finally being moved to the new rules for pay at pump charges. You can read a little more about what this means in this blog post by Daniel Chatfield. 
I’ve shared the feedback here in the community with a couple of people involved in this situation. While there are certainly a few things we could have done a little better but I hope that you’ll appreciate the transparency from our side, even if we had very little to report over the weekend. 