Can I enter an enduro race on a hardtail mountain bike?
Yes, unless they say no.

The "Spirit of Enduro" is to include all riders, of all abilities, on all bikes. Since there are guys who can ride crazy fast on a hardtail down a downhill trail, you can certainly ride yours in an Enduro race. However, you might be putting yourself at a disadvantage compared to the pro's or if you are looking to be competitive.

That said, if you take a carbon-fiber XC race bike to an enduro race, crash, and break the frame, that's your own fault. There is such a thing as having the right tool for the job. Taking an AM hardtail with a more raked-out head angle and med/long travel fork would be the best thing.

There's also the trail itself and this can vary widly. Within one race I rode trails that were fairly tame, but fast and flowy, to trails that were super steep and loose with a lot square edge rocks and whatnot. An all around trail bike will be a happy medium here. Plus, look at how much climbing you will be doing. A 2 hour pedal to the race start on a mushy 150mm FR bike isn't that fun (trust me, I did it), where as on a hardtail you'll just think of it as a nice warmup!