Is the startup requiring the noncompete just because that's what everyone else does? Often, when a company is requiring a noncompete, what they're actually trying to do is to prevent the use of proprietary information by competitors. If that's the case with this one, then maybe they'd be willing to use a nondisclosure rather than a noncompete.
These are just the thoughts I go through when I'm faced with one of these things. You are a different person with different needs, of course.
The solid advice I have for you is to talk to an attorney with experience in employment matters if at all possible to get his take on what that particular agreement means for you, and to think about the whole thing very carefully. For instance, if you'll be locked out of sorts of businesses that aren't of much interest to you anyway, a noncompete with this startup might not be big a deal.
Going to work for a startup is already taking a gamble in the first place. Being locked out of similar businesses should you leave can be a big ask of someone who's already taking a risk.
If that's the clause, then 100% don't sign it. I've never heard of a noncompete that locks you out of an entire industry before. More typically, a noncompete restricts you from working at companies that directly compete with the company hiring you.
Personally, that they'd even ask for something that extreme, even if it can be negotiated to be less onerous, would put me off of working for them. I'd take it as a sign that they're a bad company to work for.
