It shouldn't really because 'snakes' is a countable noun, but in every day spoken English you're less likely to hear 'the only thingS I'm afraid of ARE snakes'. In this case the word 'snakes' is being used as a singular, so yeah you're good. It's a natural sounding sentence.

You could say: The only thing that I am afraid of is snakes... or The only thing I'm only afraid of snakes

The only thing I'm afraid of is snakes.

It is correct!

The only things iam afraid of are the snakes