It's a tale as old as time and one of the most common things we as stylist hear on floor. "My old salon said to come with my hair dirty" but this is simply not true. If you're coming in for a colour service we always recommend coming in with hair that has been washed the night before max two days.
The main reason why very oily hair can hinder your colour service:
- it takes your colour longer to process as the lightener/colour has to lift through the oil/dirt before lifting to your desired colour. Imagine painting on a canvas covered in dust, dirt, and products . You could get the job done, but it may not be as pure as it would have been if the canvas was totally clean.
- build up of products/oil/dirt will prevent your colour from lifting evenly and lead to un predictable results.
- Assessing your hair will be harder as the build up of oil wont show your previous colour bands and can it will make your natural colour appear darker.
- Grey coverage: when moisturising be careful to not wipe your skin care into your hair. This will cause a barrier on the hair and your colour might not take to your hair. Leaving those sparkly hairs popping though.
When in doubt just ask your stylist for advise. 
If your just coming in for a cut or blowdry then it's totally fine to skip wash day and come in for that scrub you have been dreaming of.