Is it possible to change player faction?

Sorry, no. The faction depends on what you choose per world basis. You would choose to either Nod or GDI. Though I would suggest for a research option of the opposite MCV, which would allow you to research the opposite faction's units. All of this for 10x the amount needed for research point and credits.

As @Shinerplunderer said, you can't change your affiliation after you joined a world. Once you started your army you have to stick with it. Its not intended for players to change factions at any point after the start.

It would be considered OP if a player could obtain a base of the opposite factor. If a player were to obtain one, the base's expensiveness should be based on how OP it is to obtain the opposite base. It is up to the developers if they wish to implement my idea. The Research point and credits requirement should be decided by the developers as well, maybe like 10x or 20x or 50x.