To disable group request alerts on Instagram, visit your Profile, and click on “menu” in the top-right corner. Then Settings > Notifications > Direct Messages. Click on “Off” under Group Requests. At the very least, you will no longer receive a notification whenever you get added to a group.
Alternatively, you can also try Settings > Privacy > Messages. Under “Allow others to add you to groups,” tap the radio button for “Only people you follow.” This way, you cut down on getting added to Instagram groups by random strangers on the platform.