Is there a way to auto-generate GetHashCode and Equals with ReSharper?

Since you asked if also Visual Studio can do that: since XI.2017 it finaly can generate something useful.

Using ctr+. inside class and choosing "Generate Equals and GetHashCode"

See https://stackoverflow.com/a/48441971/4547594

Yes, Resharper can do that. With cursor inside your type, open the “Generate code” menu (Alt+Ins depending on settings or Resharper -> Edit -> Generate Code), and select “Equality members”:

This opens a window where you can select which members are used for equality, along with some options about the generated code (e.g. should your type implement IEquatable<T>):

If you start with a simple type with two properties:

class Person
{
    public string FirstName { get; private set; }
    public string LastName { get; private set; }
}

Then the generated code may look something like:

class Person : IEquatable<Person>
{
    public string FirstName { get; private set; }
    public string LastName { get; private set; }

    public bool Equals(Person other)
    {
        if (ReferenceEquals(null, other))
            return false;
        if (ReferenceEquals(this, other))
            return true;
        return string.Equals(FirstName, other.FirstName) && string.Equals(LastName, other.LastName);
    }

    public override bool Equals(object obj)
    {
        if (ReferenceEquals(null, obj))
            return false;
        if (ReferenceEquals(this, obj))
            return true;
        if (obj.GetType() != this.GetType())
            return false;
        return Equals((Person)obj);
    }

    public override int GetHashCode()
    {
        unchecked
        {
            return ((FirstName != null ? FirstName.GetHashCode() : 0) * 397) ^ (LastName != null ? LastName.GetHashCode() : 0);
        }
    }
}