Neutral contrast is all about not drawing attention away from your content. It's like the design equivalent of a beige wall in an art museum: it doesn't scream "look at me!" but still manages to make everything else on the page pop.
Here are some examples of neutral colors that won't clash with your content:
Grey
Beige
Light Grey
Remember, neutral contrast is all about subtlety. Don't be afraid to mix and match these colors to create the perfect balance of attention and non-attention.