When you are maintaining the social distance, you are not social distancing.

[Dilbertian]

You are socially distancing.

In 'social distance', 'social' is an adjective.

But if you change 'distance' from noun to verb (perfectly legitimate), 'social' becomes an adverb and the expression should therefore be 'socially distancing'.

I know, I know: I'm forlornly shouting into the wind. Do you hear my forlorn shouting?

Yes, but people saying "I am social distancing" shows that the noun phrase "social distance" has been turned into a verb, just if you do a slow roast, you would say "I slow roasted this" not "I slowly roasted this". (Sorry, best example I could think of from the top of my head).

Well yes, I see your grammatical point, but there must be absolutely gazillions of other examples of this in common usage, in addition to DadDadDad's example.

This pedant would say "I roasted it slowly"

Though I concede that, like I say "pressure-cooked", I might occasionally say "slow-cooked". Ugly, though.

Like I said: forlornly shouting.

Thank you!

While we are at it, you just went for a walk. No need to say 'socially distanced' walk.

Hmm... I'd happily say 'slow-roasted'. I would probably say 'socially' with the verb 'distance' myself, but it's not a hill I'm prepared to die on, or even a wind I'm particularly bothered about shouting forlornly into .