There are no hourly buses to Lisbon departing from the main bus parking lot. Let me repeat that. There are no hourly buses departing from the main bus parking lot in Obidos. I confirmed this twice at the TI office. Also, the hourly buses do not go to Sete Rios but to Campo Grande bus terminal and metro stop in Lisbon. See this https://www.obidosportugalguide.com/tourism-guide/Lisbon-to-Obidos-bus-car-train.html.
Outside of the main gate at Obidos, a street intersects North of the TI and public WC called Rua Jaoa D'Ornelas, which descends to a city bus stop. Here the Rapida Verde bus takes passengers hourly from Obidos to Campo Grande terminal in Lisbon. The ride is 50 minutes.
Conclusion: There is nothing wrong with going to Caldas da Rainha or Obidos by train. Just realize that you will have to call a cab to pick you up and take you to a hotel in Obidos. Taking a cab to a hotel in Obidos is the only way. Otherwise you are going to have to drag your bags over the ancient streets to your hotel, fighting tourists the entire way. A taxi will drive in Obidos and drop you at your hotel door.
Other than that Obidos is a day trip from Lisbon, so if you want to go to Obidos, do it as a day trip from Lisbon and go luggage free.
Thanks to the OP for emphasizing the bus & train situation for those (like me) who might have glossed over the report in the RS Guidebook, and for supplying some important facts about transportation. I will be giving more consideration to traveling to/from Obidos.