You can set your Instagram to private and even if friends from Facebook see that you have an account there they can't just view your content. They'd need to send a follow request to do that.
IG can easily still be a private space. I don't accept everyone who's on my friends list from Facebook.
e: Also, while it's potentially more work there's nothing stopping you from having multiple accounts on Instagram. The UI is actually pretty simple when it comes to swapping between more than one as needed.