We do not recommend DMing every new follower. Instagram might view this as spam activity. And this might lead to soft action block prompts, which can cause slow downs in growth. Also, please don’t use an automation software / 3rd party app to do this. Instagram dislikes all kinds of automation, and it could lead to actions blocks, accounts suspension, or worse.
You can safely DM 3-5 new followers per day, if you wish. We do not recommend sending DMs to more than that. If you’re using this as a strategy to generate leads, creating a personalized opener helps ignite interest while also keeping you safe from Instagram’s spam detection algorithm.