Local opposition, page-60

Regarding your question "It seems (though I'd be grateful for more information) that they control the municipal general plan which is presently incompatible with mining in the zone where the INF pit is planned. I don't know whether that means that, unless that council agrees to vote to change that general plan, the project simply faces a red light. Could permission from a regional or national level override the city?":
In the past (2018) Infinity already tried to modify the general plan but it was dismissed.
If the EIA gets green light from the Regional Mining Authority it still does not mean they can simply override the City. The process is complicated and legal experts expect the case to end up at court.

Regarding your question "Significantly, the platform appears to have the support of the Mayor of Caceres, Luis Salaya. But what kind of politician would let such an opportunity slip by?"
The Mayor got also voted for being against the mine (his conservative predecessor already opposed the mining project). Actually almost all of the city councils are against it. In the 2019 municipal election campagne the mining project played an important role. So there seems to be a democratic based consensus among the citizens that the mine is bad for the city. Although some here play the opposition down to some environmental radicals. The platform raised around 35.000 signatures against the mine. For a city with 100.000 this is quite significant.

When I read through the comments , I wonder if any of you really knows what it would mean to live next to an open pit mine that causes reduced air quality, noise and the destruction of a popular natural hiking zone. This is even mentioned in Infinity's own EIA published here: https://www.ayto-caceres.es/transparencia/urbanismo-y-obras-publicas/estudio-mina-valdeflores/ (parte IV - p.42) . Not to mention the risks of water pollution (in an already very dry area) and toxic residues left behind. As the mine is so close to the city - less than 3 km to the historic old town that is listed as UNESCO world heritage - it is quite logic that a majority of the residents do not want it. Me, personally, I would not. Even less now as the battery industry will be installed in Catalonia as was announced a few days ago (https://www.pv-magazine.com/2021/03/05/spain-joins-the-gigafactory-race/) and Cáceres would be somewhat like a 3rd world region providing raw materials without being able to develop a sustainable industry. It is logic for a local politician in this case to bet on tourism and agriculture instead for a short term (25-30 years) project based on explotation of a finite mineral deposit.