Is the air in aircraft cabin toxic?
It seems this is a fairly new issue cropping up and I have been able to find some credible research on the topic (i.e. from official aviation authorities and not news outlets or lawyers websites...) but all of it is pretty recent. The CAA seems to be aware of the issue and has some information on it here. The two studies they link were published in 2017 so the topic seems to be recent, you can find the full text here and here.

The Australian authorities via CASA conducted a pretty hefty study on the topic in 2007 and came up with a list of 37 recommendations which includes the development of an anonymous online reporting system. 


  
  That the Australian Government, through CASA and the ATSB, sponsor and
  fund the development of a single, central, internet-based,
  confidential reporting system on cabin air contamination incidents to
  be co-ordinated and operated jointly by CASA and the ATSB. To improve
  the reporting and monitoring of cabin air contamination incidents,
  this system should have web-based forms to facilitate the collection
  and collation of data from all authorities and companies responsible
  for cabin air contamination incidents that would enable the data to be
  tabulated into a de-identified and unalterable uniform document that
  could be accessed and utilized by all stakeholders.
  


They also are setting some resources aside for studying long and short term effects of an event 


  
  That CASA in association with the Department of Health and Ageing
  (DOHA), the Institute of Health and Welfare or the NHMRC sponsor a
  project to define possible criteria for case definitions for short
  term and longer term health outcomes following episodes of cabin air
  contamination.
  


Clearly the CASA sees this as a real issue. 

The FAA published a safety advisory on the topic in March 2018 and is clearly acknowledging the issue.  

Its worth noting that most of these studies and claims refer to an "event" in other words a notable time when there was a fume event implying that this is not a constant occurrence. On the flip side, cabin air is actually pretty clean, as discussed here and researched here. Interestingly this CDC study seems to point to the slightly lower oxygen levels and more importantly tight quarters with a lot of other people to be factors in health issues on aircraft. They did this by comparing flight attendants with teachers who also work in lower circulation, high person density environments.