Does EMDR legitimately treat any condition? Are there any studies not funded by friends or beneficiaries of EMDR that prove it helps with a strong p-value?
TLDR: EMDR seems to be equally efficacious to other therapies.

Davidson &amp; Parker, (2001) conducted a meta-analysis.


  Eye movement desensitization and reprocessing (EMDR), a controversial treatment suggested for posttraumatic stress disorder (PTSD) and other conditions, was evaluated in a meta-analysis of 34 studies that examined EMDR with a variety of populations and measures. Process and outcome measures were examined separately, and EMDR showed an effect on both when compared with no treatment and with therapies not using exposure to anxiety-provoking stimuli and in pre–post EMDR comparisons. However, no significant effect was found when EMDR was compared with other exposure techniques.


Rothbaum, Astin, &amp; Marsteller, (2005). Looked at EMDR with Rape Victims.


  This controlled study evaluated the relative efficacy of Prolonged Exposure (PE) and Eye Movement Desensitization and Reprocessing (EMDR) compared to a no‐treatment waitlist control (WAIT) in the treatment of PTSD in adult female rape victims (n = 74). Improvement in PTSD as assessed by blind independent assessors, depression, dissociation, and state anxiety was significantly greater in both the PE and EMDR group than the WAIT group (n = 20 completers per group). PE and EMDR did not differ significantly for change from baseline to either posttreatment or 6‐month follow‐up measurement for any quantitative scale.


Seidler, &amp; Wagner, (2006) conducted another meta-analytic study.


  The superiority of one treatment over the other could not be demonstrated. Trauma-focused CBT and EMDR tend to be equally efficacious. Differences between the two forms of treatment are probably not of clinical significance. While the data indicate that moderator variables influence treatment efficacy, we argue that because of the small number of original studies, little benefit is to be gained from a closer examination of these variables. Further research is needed within the framework of randomized controlled trials.


References

Davidson, P. R., &amp; Parker, K. C. (2001). Eye movement desensitization and reprocessing (EMDR): A meta-analysis. Journal of consulting and clinical psychology, 69(2), 305.
DOI: 10.1037/0022-006X.69.2.305 PMID: 11393607Free PDF: https://pdfs.semanticscholar.org/d703/9ab57fabe1a3b0aee33bf558b95cf228700c.pdf

Rothbaum, B. O., Astin, M. C., &amp; Marsteller, F. (2005). Prolonged exposure versus eye movement desensitization and reprocessing (EMDR) for PTSD rape victims. Journal of traumatic stress, 18(6), 607-616.DOI: 10.1002/jts.20069FREE PDF: https://pdfs.semanticscholar.org/d5cd/abbee19ef9886327fd77be0587e6826842d6.pdf

Seidler, G. H., &amp; Wagner, F. E. (2006). Comparing the efficacy of EMDR and trauma-focused cognitive-behavioral therapy in the treatment of PTSD: a meta-analytic study. Psychological medicine, 36(11), 1515-1522.DOI: 10.1017/S0033291706007963