"Make money off of" vs. "make money out of"

I'd prefer the second one, although not because of the reason you cited.

"Make money off (of) something" is different from the phrasal verb "make off."

Both "make money out of" and "make money off" are actually right.

For me though, "make money off" may also be used to imply an unscrupulous method of generating income.

ex. make money off my friends, make money off the mentally ill etc. 

This seems like another US/UK split. Looking at Ngrams, "make money out of" is the traditional way of saying it, but in the U.S., "make money off (of)" has now overtaken out of in frequency. From Ngrams

In the U.K., out of is still far more common. Since it's still correct in the U.S., you should probably choose out of if you're deciding between them.

Since the phrasal verb make off does not take an object, the meaning run away is impossible for "make money off"; to use the phrasal verb with money as an object, you would need to say "make off with money".

To me, the second one makes impression of being too literal. Like minting coins off arcade tokens, or printing notes. What about making money on something?

Off of is a compound preposition common in London (and possibly elsewhere in the UK) but deprecated by purists, who strongly prefer either from or in some cases off. Said purists do not appear to have any objection to out of.

In your example, out of or from are idiomatic. One does hear off or off of in this use, but they are not standard.