I don't think working for a start-up is a particularly risky thing to do. While I won't deny there is some risk, the risk largely boils down to whether the company will be able to raise its next round of funding or not, or whether it will ever turn a profit.
Personality type matters. If you have a fairly clear sense of where you want to be in 10 years' time and want to build your career in a linear, predictable fashion, then a job at a start-up probably isn't right for you (unless you want to become a venture capitalist). Most start-ups expect to go from "zero" (i.e., an idea) to IPO within a 10-year period, but many never make it to that point, and, when this inevitably happens to a company you work for, "failing forwards" can present you with unexpected opportunities that may not align with the ideal "next step" you'd considered.
If you want to work for an organisation that feels more anarchic than bureaucractic, where staff ask for forgiveness rather than permission, that empowers every employee with a very real responsibility that can directly impact the company's bottom line, then you should consider working for a start-up. You may not need to compromise on the things you think you do, too.
At risk of stating the obvious, not all start-ups are the same; a pre-seed-stage start-up is markedly different to a Series B-stage start-up. I've only ever worked for pre-seed-stage start-ups,[1, 2] in part because I've been prepared to trade risk for ownership (i.e., equity) in the most extreme way available to non-founders, but there are many very well-paid, exciting opportunities to work for companies with $30+ million in funding and a much clearer path to profitability or, at the very least, the next funding milestone.
I think I'll return to this because it's worth talking about in more detail.