So long as they're well within each other's Hill Spheres I don't think the sun should be an issue any more than it is with our moon. (The moon's orbit is about 1/4 of the way to Earth's Sphere) And Earth already orbits our combined center of mass with the moon, it's just that the size discrepancy (it's only ~1% of our mass) means that's still within Earth's volume, about 3/4 of the ways up from the core.

Forming would be a different question, but e.g. if Theia had been considerably bigger (or faster?) when it hit proto-Earth the "splash cloud" might have coalesced into two much more similarly-sized sister-planets.

Exactly the same size (to how many significant digits?) would indeed take crazy long odds. But within 10% or 20% is probably not too outlandish.