As you’ve figured out, Entity Framework can’t actually run your C# code as part of its query. It has to be able to convert the query to an actual SQL statement. In order for that to work, you will have to restructure your query expression into an expression that Entity Framework can handle.

public System.Linq.Expressions.Expression<Func<Charity, bool>> IsSatisfied()
{
    string name = this.charityName;
    string referenceNumber = this.referenceNumber;
    return p => 
        (string.IsNullOrEmpty(name) || 
            p.registeredName.ToLower().Contains(name.ToLower()) ||
            p.alias.ToLower().Contains(name.ToLower()) ||
            p.charityId.ToLower().Contains(name.ToLower())) &&
        (string.IsNullOrEmpty(referenceNumber) ||
            p.charityReference.ToLower().Contains(referenceNumber.ToLower()));
}