Updates below in chronological order (most recent last)
UPDATE (29-Apr-2020). One taxi driver told me that both border crossings at Tapachula are closed. Another taxi driver told me that the border crossing at El Carmen (the smaller of the two) can still be crossed without problems. Both taxi drivers claim to have contacted their friends at the border to make sure. Our embassy says that the border crossing is still open (they did not specify which one).
UPDATE (29-Apr-2020). Both taxi drivers said that the border crossing at La Mesilla is still open (= allowing tourists to cross into Mexico). This is the crossing on the way to San Cristobal. The embassy discouraged that crossing because of "drugs traffic" although we had no trouble crossing it into Guatemala from the Mexico side back in Feb when the tourists shuttles were still running. Another problem with this crossing is that it is still 3-4 hours by car to San Cristobal after crossing the border, and I do not know what the taxi situation is on the Mexico side. Guatemala taxis are not allowed to cross. Thus, the safest option would be to pre-book a Mexican taxi from San Cristobal to meet you on the other side.
UPDATE (30-APRIL-2020) We got a message from a taxi driver who attempted to bring some tourists to the El Carmen border crossing. He says: "Yesterday (29-April) we went to the border EL CARMEN .. no way , they didn’t let the people into MEXICO …. So , no confidence at all that this will be possible . Maybe if you can work something out with your embassy … (they call it a salvaconducto) or if a humanitarian flight could be organized .. but this is way out of my possibilities …. Pretty sure you are stucked in the country , being able to leave …… in a month or so … nobody really knows."
UPDATE (30-APRIL-2020) The consulate from my local country says: "Yesterday I checked with the Mexican consul and he says that indeed at 'at this time it is very difficult'"
UPDATE (30-APRIL-2020) Another taxi driver says that the only open border crossing at this time is "La Mesilla" (the one which our consulate advised against).
UPDATE (1-MAY-2020) Even if you get to Mexico City, most (or maybe all) hotels are closed. There is some information on the Internet saying that AirBnB is also forbidden in Mexico City, although plenty of AirBnBs are still being listed and at least some are still accepting guests (but not all, make sure you message the host to check before you book.)
NOTE We are abandoning our plan to exit Guatemala overland via Mexico, so I will stop posting updates.