No matter how fastidious a beader/embroider you are – no matter how many times hands are washed – the natural oils or even just the many times of touching a light colour fabric – the fabric will get dirty.
Your touch over time will dull the pristine newness of the fabric you are using. There’s no way around it. It will happen.
So the only way to help prevent this is to either cover as much of the fabric as you can with cling film or wear fine cotton gloves. Or both. I use both when the fabric is hooped up and just a glove on my holding hand when out of the hoop.
My holding hand is not the hand that holds the needle i.e. my dominant hand. I am right handed so I wear the glove on my left hand.
But these gloves, easily and cheaply available on the internet, are unfortunately a one-size-fits-all and I have had to alter the shaping of them. Luckily I only use one at a time and the gloves do fit either hand.
But one thing I do is to just nip the end of the thumb off. This lets me use my thumbnail to press down on the fabric when needed.