Assuming two identical twins want to swap their passports (e.g. to travel using the other guy's visa or to make visa runs easier) - would there be anything to stop them?
Some visas do record the applicant's fingerprints but would you really be banned from entering if just the fingerprints mismatch?
Does anything stop identical twins from traveling on each other's passports?
Technically, yes. It is illegal, that's the one thing that will stop most people.
In practical terms, can identical siblings use each other's credentials in many scenarios, yes, of course, especially if the picture is at least a year old.
The inclusion of multiple authentication factors though, such as fingerprints, make it much more difficult, especially when the intent it to verify identification.
However, keep in mind that verifying fingerprints in questionable situations is not a quick process. The software is very good at matching but an officer may still needed to verify the match. I would not be shocked (meaning I am admittedly speculating) to find out this step was skipped if the initial entry interview raised no suspicions.
There is a good chance of being deported/removed if your fingerprints don't match. You will certainly be scrutinized more until they can confirm (based on a balance of probabilities) you are who you say you are.
Answer is based on experience. A family member's fingerprints couldn't be confirmed on one trip to the UK. They gave her a paper telling her they were deciding whether to let her enter or not.
I think the UK needs to upgrade their fingerprint machines. On many occasions it takes several tries until the fingerprints match.