Is it possible to switch sides in Ingress?

Yes, but you have to contact Google and it takes about a month or two to complete. Google/Ingress will only allow one switch per player, apparently human approval must be involved in the process somewhere.

I switched factions because I didn't realize that the Rebels represented Luddites which I find philosophically annoying, it took many weeks for Ingress Support to finally change it.

Your account get's largely if not totally reset.

Here's the link to the help center where you can change it: Ingress Support

From the Help Center on changing accounts:

If a faction change application is accepted, that player’s Portals, Resonators or other items obtained will be lost, and the player will be returned to Level 1, 0AP. If one of your teammates changes allegiances, you may see NIAOPSDAEMONX destroying entities. Do not be alarmed, all traitor activity must be wiped. Some of your related entities may be destroyed in the process, but it is for your own good and the security of your faction.

with the fraction change request you get to keep your badges but loose everything else. If you don't care about that you can do is what I did which was request to delete the account. It took a few hours, your email will be banned so you will need to use another one and boom it's done.

I need to mention that because you have to use another email, the vetting process to get into the groups will require some explaining from you because the (oh my god you must be cheating!) sign out button will forever show it's self in the [OPS]-device setting. If they will listen, just explain what happened and if they still don't believe you, just show them what happens when you try to log in using the original email (in-case you're wondering it won't work).

If there is still an issue with the vetting process just play the game on your own and let your links, fields, and take downs speak for you.

Remember it's a game, your supposed to be having fun with it