If the site asks for your own Instagram login credentials, it is likely a phishing attempt to hijack your account. Privacy Violations:
Often, people go private to avoid spam. If you engage authentically with their public posts or stories (if they have any), they may follow you back or accept your request. Igmods View Private Instagram Profile App
Apps and sites like Igmods are widely considered or "malware traps" by security researchers. If the site asks for your own Instagram