Kinda but not really, they're both made from glass fibres, but are a very different product that serves a very different purpose. Fibreglass typically comes in a flat cloth, and is used with resin to create something structural.
I worked on a few buildings where they used straw balls lenght wise. They had meter thick walls and it's very efficient. One of them only had a tiny wood stove
Haybale homes have been around for ages, mum said they popular in the the 70s with the earth loving movement, and I recall them getting popular on pinterest again in 2012ish with the eco house movement.
You stack the bales, run insulated cables and plumbing as needed, then render over the whole lot.
The cob or other earthen plaster incorporates clay or livestock manure which add hydrophobic and polymeric properties, which then air-cures to seal out moisture, and it's thick so if it gets wet it has to get really wet to penetrate the hay. Ideally these also have large overhanging rooves to sheet away rain.
To all the comments saying this is just straw insulation: it's more than that.
Compressed straw as building blocks is a thing now. Apparently it's strong and fire retardant too, though I don't know how much treating and cladding it needs above just being compressed.
Usually the straw block is made with a big motorised machine, but I've seen a hand-operated straw block press, with a great big long pole as an enormous lever. And the building made from its produce: a two storey building with conference hall and kitchen/accommodation. I think only the conference hall half was made with the straw blocks; the other half is interlocking bricks (like Lego 1-by-2s) also made on site.
Doesn't using straw in roofing or insulation spread bed bugs? I remember reading how the little monsters used to spread in medieval Europe that way, and in their straw mattresses.