Funds, mostly. Investors who want a large stake of control and see intrinsic value in a TNC outside of the numbers. People who buy into California math. People buying a $42 lottery ticket. ML trading algorithms who have a tensor weighted heavily on "unicorn going public" that ends up equating to "Buy". Family or friends of employees that want to buy so they can "root for the company" (Yes this sounds ridiculous but this happened to a personal friend of mine and his mother still always asks why the stock is down 300% from when she bought it, and when she can expect for it to go up.)
There's a lot of reasons why people would buy Uber. But for anyone who is investing safely for retirement, I think it's easy to see that this is not an investable company at the moment.
IPOs aren't even added to the indexes until it's been some months since their IPO.