I thopught at first that it’s possible, but thought better of it. Follow along with me. – imagine the potential energy surface. If you make a model in that shape you can roll a ball aeround it and it will mimic an orbit (a lot of planetariums and science museums have these. Heck – I’ve seen shopping malls with similar things that encoiurage you to spin coins into them to collect for charities.) The difference is that this well would have two pits in it, one for each star. You’d also want to spin it, to mimic the effect of rotation (those two stars better be rotating about a common center, or gravity will suck them together.)
Now, if that rotation wasn’t there, I could easily see a figure-8 orbit developing. You just have to finesse rolling that imaginary ball at the right speed and angle to get it to go through the exact center of the system.
But with the system rotating, you’re outaluck. The ball (planet) has to be rotating about the center, too, so it has to maintain constant angular momentum. The closer it gets to the center of the system, the faster it has to go. For zero distance (passing through the center) you have to go to infinite velocity. Ooops.
Another way of looking at that it that you can, instead of rotating your model, simply add a “centrifugal potential”, in the form of an upward-pointing funnel in the middle of your model. With a single well and a cebtrifugal potential you end up with a big “spike” sticking out of the middle, dropping to a ring-shaped trough arounbd that, then climbing on the outside. Your planet will sit in the trough that defines the orbit (you don’t have to spin the ball around the potential well – your cetrifugal potential does that for you). You can see how a stable radius is defined by the radius of the trough. If you “rock” the ball back and forth in the trough, you get an elliptical orbit (the trough is shallower away from the center of the centrifugal potential).
With a two-mass system having two pgravity wells and one centrifugal anti-well, you can see how you’d never get to the center. Hence, no figure-8 orbits. The height of that centrifugal spike depends on your velocity/angular momentum. If it’s high enough, all your orbits are distorted circles or ellipses around both stars. If it’s low enough, however, you can get some eccentric shapes. But that spike in the center of the system forbids figure 8’s.
By the Way, Lagrage Points are only stable if most of the mass is in one of the two gravity wells. Two equal masses don’t fulfill that requirement, so the “Lagrage Points” of a two-equal-star system aren’t stable.