Great question!
Linen and
nettle fibres are your most
solar resistant natural cloth. That's why they were so popular for drapes in the past. But expensive. Maybe you can get some at a second-hand shop as they sometimes have old table cloths.
Next up, I would say wool and hemp. Wool lasts about 300 hours of direct sunlight, before beginning to decay - that's about two summers average - maybe four where I am, less where the sun is stronger. However, if the wool was processed in a large, industrial scale mill, I would cut that estimate in half due to some of the chemicals used in the processing. Hemp depends on how it was processed. Sometimes they use a harsh chemical to soften the hemp which causes it to degrade very quickly - one to two years. Less common, but sometimes still available, are traditional/mechanical processed hemp which can last four to 6 years in those conditions.
Cotton is probably the least durable in these conditions, but possibly my first and last choice. It cheapest and it degrades quickly. You can often find cotton sheets in secondhand shops. I would expect this to last one year for something like sheets. Duck cloth (a kind of canvas good for making tents) lasts me about three years but doesn't allow enough light through for the plants, so I just put this to shade during the heat of the day, not all day. Something I've been worried about is the high amount of chemicals (both agricultural and manufacturing) used to make cotton cloth. I'm wondering if they will dissolve into the soil when I
compost the cloth. For this reason, I'm moving away from using cotton in the garden and trying to find more linen.