Mexico regulates drones through the aviation authority AFAC, but official registration is practically reserved for Mexican citizens. For tourists, private use of small drones away from archaeological sites remains the realistic option.
A maximum altitude of 122 meters is allowed in uncontrolled airspace, always within visual line of sight (VLOS), night flights aren't permitted. A minimum distance of 9.2 km from airports and 900 meters from heliports must be kept, flying over gatherings of 12 or more people is also prohibited.
Flying is generally prohibited over all sites managed by the heritage authority INAH, including Chichén Itzá, Tulum, Cobá, Uxmal, Teotihuacán and Palenque. Rangers specifically watch for drones with binoculars, confiscations happen regularly. Professional filming permits are theoretically possible but cost up to around 10,900 pesos per day through INAH.
Without proof of purchase, problems can arise at customs, sometimes up to 16% tax on the replacement value has been demanded. In individual cases drones have been fully confiscated, so it's worth keeping proof of purchase and a short explanation of private travel purpose on hand.
Civil fines range from 200 to 5,000 UMA (around $870 to $25,000), unregistered operation can be fined up to 400,000 pesos (around $20,000). AFAC can additionally confiscate the equipment.
For private footage at beaches or in nature away from ruins, a small drone is usually fine. At Maya sites, I'd leave the drone at home entirely, the risk of confiscation there is high and actively enforced.