Yes, it can be considered controlling and weird if your girlfriend has access to all your emails and social media accounts without your consent or without a valid reason for doing so. Privacy is an essential aspect of any healthy relationship, and both partners should respect each other's boundaries and personal space.
Having open and honest communication in a relationship is crucial, but that doesn't mean giving up all privacy and personal boundaries. Trust is the foundation of a strong relationship, and if your girlfriend feels the need to have constant access to your private communication channels, it may be a sign of trust issues or control.
It's important to have a conversation with your girlfriend about boundaries and privacy. Let her know how you feel about this invasion of your personal space and express your need for trust and respect in the relationship. If she doesn't understand your concerns or is unwilling to respect your boundaries, it might be a red flag that requires further discussion or possibly seeking advice from a professional counselor or therapist.