Visited just recently (November, 2021). Since the site was carefully decribed by other travellers I will focus on transportation warning so you may avoid problems while trying to get there without your own car.

Arrived in the afternoon (21.11.2021) at Xpujil and immediately started to organize a transport for the next day to Calakmul ruins. As there are no public transport directly to the archeological site you have to arrange something on your own. There are several options. The easiest seem to be tour agencies offering full day package (transport, food, guide) for 1500 (or more) peso per person. Taxis goes there for similar amount of money (or if you negotiate hard for a bit less) – this include 3 hours waiting time on the place. This option is paid by trip so if there are 3 -4 persons it might be the best solution. Other option is to go by bus from Xpujil ADO bus station to entrance of Calakmul National Park (some 60 km from Xpujil, Entronque a Calakmul) and try to organize transport from there (additional 60 km to Zona Arqueologica).

As realized the options I tried to find an agency and ask them for transport. Just opposite my hotel in Xpujil (Becan Hotel) I found an agency - Tour In Calakmul By Abel, google coordinates: 18.50806987416214, -89.39426131904403. It looked as normal agency, the person inside was very helpful and communicative (he spoke very good English). After short negotiations he reveled that next day he had a tour to Calakmul so it was possible to go with them – just transportation, no package. Good for me. Finally we agreed on the price 400 peso as I wanted to be left on the main highway (Entronque a Calakmul) – later on I wanted to go to Escarcega / Campeche. In the meantime another tourist from Canada came to the agency and realized it was possible to go to Calakmul on the next day. As he wanted to return to Xpujil he was about to pay 500 peso so he did. Received a receipt for that. Fortunately I did not pay anything but promised to pay next day while the transport would be organized.

Next day, as agreed we (together with that guy from Canada) have been on the spot at 6 a.m. but there was nobody waiting for us. The office was closed and nobody from the agency answered the phones. We waited until around 7.30 and realized that we had to organize alternative transport. I went there by bus while Desmond and the people who had paid for the package tour decided to go by taxi.

Personally I lost only a lot of time and some confidence in people but I was curious how this situation ended (both Desmond and the people from the package tour had paid deposits for the service that was never executed). It seems that the agency that was initially reliable with good opinions now changed into normal scam as they did not return the money.

You can read that on Tripadvisor (by using name Tours in Calakmul Abel) – three recent reviews indicate scam with full description

https://www.tripadvisor.com/Attraction_Review-g635715-d20367719-Reviews-Tours_in_Calakmul_Abel-Xpujil_Town_Yucatan_Peninsula.html

and Google – using the name: Tour In Calakmul By Abel – 5 recent reviews are from cheated persons

So what are the solutions ? Probably the easiest way is to go there by rented car or with someone who you know. Good option is to use local taxi (ideal for 4 persons) as you share the cost and usually pay after the service is executed. If you are lucky you can try to hitch-hike (or go by bus to Entronque a Calakmul and hitch-hike from there). Personally I did the latter option - bus from Xpujil goes around 7.30 in the morning, so after an hour you can reach Entronque a Calakmul. After buying tickets - National Park fee and local community tax - total 150 peso (additional 80 peso you will pay for a ticket to enter archeological site) I found a local Uber/taxi - for only 200 peso he agreed to go to Zona Arqueologica and back. Of course I paid at the end of a trip. From Entronque a Calakmul there are buses to Escarcega or Xpujil / Chetumal, not very frequent but it is the best option if you travel without your own transport. For timetable you can try to ask at the ticket booth. 

Places on the photo, bottom left, than clockwise: Estructura 2 (view from the top), Gran Acropolis (residential quarter), Estructura 1, Gran Acropolis (the pyramid)