You can't tell, but a vet or shelter can (kind of). If the rabbit has a microchip, a phone call will likely identify the gender, and history of the rabbit. Without a microchip, if you can't find testicles assume it is a young rabbit (of either gender) or an unaltered adult female.
Rabbits are much like cats when trying to tell their gender. As you point out the existing question How do you tell the gender of a rabbit? is not a lot of help.
If the rabbit is a mature unaltered male he should have testicles much like a cat. You should be able to feel or see them fairly easily. Occasionally one or both testicles will not descend, but this is fairly rare in my experience, so I will ignore that possibility for remainder of this answer.
If you don't see/feel testicles the rabbit could be a:
- Young unaltered male
- Neutered male (5-6+ months to 10+ years)
- Young unaltered female
- Spayed female
- Adult unaltered female
Young rabbits are much harder to tell the gender of than adults. Their genitalia are under developed so a skilled person may be able identify they are young and unaltered but not be positive about their sex. Even if an experienced person gives a gender, there is a 50% chance they are wrong. Nearly all the baby bunnies that come to our local rescues are from siblings that "were both the same gender" when young.
So you can tell pretty well if a rabbit is in group 1 or 3, but any definitive answer would be advisory; until they develop testicles, have babies or get spayed.
An adult male who has been neutered, can usually be determined. But at our local shelter if there is any doubt they assume that it is an unaltered female. It is not unusual for a an adult rabbit to enter surgery to be spayed, and once the surgery is underway they discover it is actually a neutered male. Other than medical records you can't dependably tell an unaltered female from a spayed female on visual exam.
So for groups 2, 4 & 5 sometimes you can reliably identify the neutered male, but there is some room for error, so all are generally assumed to be intact females.
The only time you can reliably tell that a rabbit is a neutered male or spayed female is if they have been microchiped and you get their medical records. All the shelters and rescues in my area, microchip and alter rabbits before they leave, in some cases baby bunnies are too young to spay and may leave with just a microchip, but the spay/neuter is covered, the person brings the pet back and it is altered for no additional cost (actually they get a refund).
If the rabbit does not have a microchip it probably came from a breeder, and is unlikely to have been spayed. If it has a microchip you should be able to assign gender and spay/neuter status with a phone call. The only reliable definitive proofs are procreation (making babies) and surgery.