How to write a more compact ANDed conditions with if statement?
There is a standard C function for this, memcmp(). It performs a memory block compare and can be used like this: 

if (!memcmp(bt, rfid.serNum, sizeof(bt))) {
  lcd.clear();
  lcd.print("card accepted");
  digitalWrite(green_led,HIGH);
  digitalWrite(red_led,LOW);    
} 
else {
  ...
}


Ref. http://www.cplusplus.com/reference/cstring/memcmp/