It is believed that if the events of Legion take place in the films continuity, it is very likely to be taking place in the revised timeline rather than the original.
The events of Legion is believed to take place between the events of Days of Future Past ending and Logan. Possibly around the same time as Deadpool.
In Logan, Deadpool and Legion the government are heavily involved in capturing, controlling and experimenting with mutants and their genetics.
In the Logan film, the company "Transigen" control mutants (X-24 for example), use genetically modified crops to control the mutant population, capture the remaining (that are unaffected by the infertility caused by the crops), use harvested mutant DNA to create clones/offspring for government purposes.
During the Events of Legion, there is a character called Walter aka the Eye who is a mutant working for the Division that hunts David and is at war with Melanie Bird's rebellion. It is possible that Walter was created or captured by the government to help their cause against mutants much like Caliban once did for Transigen
In Deadpool, the Weapon plus facility that Ajax is in charge of is tasked with creating Mutates using serum and torture to activate latent X-Genes. It is possible Transigen's modified crops had inhibited the X-Gene so that many mutants do not have their X-Gene activated
This would explain why Wade Wilson is a mutant in the original timeline but is a mutate in the revised timeline. It could also explain why David and his family do not consider the possibilty of him being a mutant, as they are known to exist in the new timeline but are increasingly rare.
In Deadpool, an adreneline enhancing serum is used to help force a latent X-Gene to activate under extreme stress like torture, Transigen uses a serum that enhances a mutant's power such as Healing Factors but may be unstable.