An up-to-date analysis has been requested. I agree that it's desirable to integrate the study "Electromagnetic Hypersensitivity: Evidence for a Novel Neurological Syndrome" (McCarty et al. 2011) into a larger analysis. Another team, Rubin et al. were unable to replicate this study and complained to the journal about McCarty's poor controls, which launched a heated exchange of letters with each side accusing the other of poor conduct ("Letter to the Editor: Electromagnetic Hypersensitivity" International Journal of Neuroscience 2012). See this stats.SE question for further analysis.
In 2017, an edited scientific volume characterized McCarty's and other studies as follows:
To date, the results of provocation studies suggest that [self-described hypersensitivity] is not caused by exposure to EMFs (indeed, they do not provide any evidence that EMF exposure causes the reported symptoms). Yet, like epidemiological studies, provocation studies are challenged by several methodological limitations, some of which could potentially explain the inability of these studies to find an effect of exposure. One of these limitations relates to recruitment. Little is known about whether subsets of IEI‐EMF exist and so it is conceivable that the samples tested may have included a combination of both individuals who are sensitive to EMF and others who may suffer from unrelated conditions. This could result in a large amount of noise being added to the data, which would reduce statistical power and mask any real effects.
Verrender et al., Non-Ionizing Radiation Protection : Summary of Research and Policy Options, John Wiley & Sons, Incorporated, 2017. p.372.
Here is a new meta-analysis from 2016 that specifically discusses sensitivity to mobile base stations:
Klaps et al. "Mobile phone base stations and well-being--A meta-analysis." Sci Total Environ. 2016 Feb 15;544:24-30. doi: 10.1016/j.scitotenv.2015.11.009
The existing studies on this topic are highly inconsistent. In the current paper we attempt to clarify this question by carrying out a meta-analysis which is based on the results of 17 studies. Double-blind studies found no effects on human well-being. By contrast, field or unblinded studies clearly showed that there were indeed effects. This provides evidence that at least some effects are based on a nocebo effect. Whether there is an influence of electromagnetic fields emitted by mobile phone base stations thus depends on a person's knowledge about the presence of the presumed cause. Taken together, the results of the meta-analysis show that the effects of mobile phone base stations seem to be rather unlikely. However, nocebo effects occur.
In 2018, the Swedish Radiation Safety Authority published an overview of research from 2015 to 2017, "Recent Research on EMF and Health Risk". Pages 74-79 of this comprehensive overview discuss hypersensitivity. It concludes:
New publications on electromagnetic hypersensitivity, EHS, could not identify physiological
characteristics that may help diagnose or develop effective therapeutic options.
It should be noted that this overview includes statistically significant health damages related to electronic devices -- however, the evidence is strong that factors other than RF-EMF are the cause. The authors of the overview analyze each of the EMF hypersensitivity studies and find that there are damaging health effects which are worth analyzing in terms other than "hypersensitivity":
... given the inconsistency in
terms of EMF-exposure the authors concluded that the study does not support a link between RF-EMF
exposure and sleep quality, but potentially other factors that are related to mobile phone usage may
negatively affect the sleep of children.
There have also been additional studies not yet included in any published meta-analysis.