I have often seen both of these and wondered which I should use. Which has the first citation? Hippy seems the more obvious spelling and I can’t think why hippie emerged as an alternative. (One dictionary says hippy adjectivally means a woman with large hips though it seems an impossible stretch that it was to avoid confusion.)
Which would you use and why? Or are they completely interchangeable?

"Hippy” means prominent hips (I remember my ex-wife using the adjective on numerous occasions).  “Hippie” means tie-dyed shirts and peace signs.

Which would you use and why? Or are they completely interchangeable?

I would use “hippie” because that is the dictionary form and the only way I ever see it spelled.  I’m not sure why you find it odd; -ie is a common ending in affectionate/diminutive forms: birdie, townie, cutie, etc.

My impression has always been that the spelling “hippy” for “a person, usually exotically dressed, who is, or is taken to be, given to the use of hallucinogenic drugs” (OED) is chiefly or entirely BrE, while the spelling “hippie” is AmE. Certainly the first British cite in the OED, from the London Times, is the “hippy” spelling, the Times Guide to English Style and Usage (London, 1992) says “hippy, hippies”, and the New Oxford Dictionary for Writers and Editors says “hippy (also chiefly N. Amer. hippie)”, so the evidence seems to support that idea ...

Interesting; that would explain why I’m only familiar with the -ie form.  I wonder how the difference got started?

I googled “hippie Guardian” and they use hippie now. Maybe in London in the 60s hep cats picked up on the American word orally and the underground press or the uncool Times spelt it hippy never having seen it in print. The online dictionaries I consulted had both spellings and no etymology…
...has the etymology been established yet? I remember reading one about hipsters lying on their sides and getting sore hips when smoking jazz cigarettes which Dave could probably add to his Word Myths.
I don’t find hippie odd, in fact I would say I have encountered this more than hippy, though I cannot say if it is from reading a lot of American prose.  Birdie, townie, cutie, budgie, etc apply in the UK too but why is this? Because they are nouns? For adjectives we seem to use y eg loopy, dippy, fruity, shirty. But not homey in the slang sense.