Different predictions with forecast::auto.arima()

This is definitely a statistics question still so not on topic here... as

changing the data is exactly the kind of thing that can have this effect.

I'm sorry.
I disagree.
This is a question about reproducible code.
So, I don't see why it should be considered off topic.

The function returned a (2,1,0) model with drift. However when I used the
same function it returns a (1,1,0) model. There were no obvious

differences

in the code. The only thing passed to it was the data. How might this
happen?

Either a different version of R, a difference in the forecast package, a
difference in one of it's imports (which there are many), or different
input.
If you're sure the input is the same, then it must be one of the other
reasons.

I suggest reading the documentation for the relevant forecast package
functions.

The auto.arima() function alone has many arguments.
Changing their values may produce a more desirable model.