Is it possible to make a base that's impenetrable by other players?

Not reasonably

Nothing you can build in vanilla Minecraft is indestructible.

That said, Simply Sarc recently posted a video on his channel, where he shows off a way to actually make a base indestructible, using 60 Elder Guardians, which are synched up so that one of them uses his curse every second. That means thats any player in the vicinity can't not have Mining Fatigue III for more than a second at a time.

This doesn't make your base truly indestructible, but depending on the material you used for building it, it will make breaking into a base take an awfully long amount of time.

Of course, your team would also be unable to break things inside your base, but you could have a redstone-operated door which can only be opened from the inside.

In pure survival, your team would need to capture these guardians manually, which involves raiding at least 20 ocean monuments. It is also possible to synchronize the curse timers, although the video doesn't go into details, mostly because ot would be utterly ridiculous to even attempt this method of base protection.