Can I use fresh gutter water for my vegetable?

I collect the water from the eves into a barrel and YES I use it for the flower beds and food plants. Occasionally gritty sand comes from the shingles but I clean the barrel out completely in summer several times and add the sand/grit to the soil. Cleaning or using it to the bottom eliminates mosquito larva.

The barrel has a faucet to attach a garden hose so it's easy to empty.

I would think that if you have a collection barrel that collects roof run off, the heavier roof granules and debris will sink to the bottom. I would think the water at the top would be ok to use for gardens. Just my opinion,

I am 86 and my deceased grand parents lived in a house in So. Illinois. Most all the water used was, from the roof, gathered with the gutters, and piped to an above ground, about 4' by 4' box like thing filled with graded gravel and sand. This was piped to a cistern, to augment ground water as needed. So if they could use it for all household uses, why on earth would't it be fine for your garden. I would certainly not even bother to filter it, straight from the gutter, OK.

if your gutters functioning Yes you can collect and use for your garden. Those pieces of shingle in the water? If they weren’t plant safe they would not be in use. Have you considered making a rain barrel to collect the water?

Shingles are mainly tar and gravel on heavy paper. The gravel is the only thing that will likely be coming off. Perfectly safe. If there is more than gravel coming off, call a roofer because you might have a bigger problem. ;) Homesteaders do this all the time as a free water source for gardening.

A lot of people collect rain run off. My community provides two free barrels for anyone who wants them to collect roof run off. Can buy more from them also.

Perfectly safe for any use that is not going in your body. Water garden yes, cook NO! After all you will wash veggies before you use or store. DO NOT USE OLD OIL DRUM!! Many places have barrels with a top and you can attach your downspout into the barrel.

https://www.gardeningknowhow.com/garden-how-to/watering/collecting-rainwater.htm