Of late, musicians tune the sruti box to madhyama sruti mode for ragas like Sriranjani, vasanta, Abhogi, Varamu etc. which are NOT Madhyamasruti scales. My first experience with this style was when Veena Chitti babu used M for Hindolam (samajavaragamana) and Sriranjani (sogasuga).
While using the traditional tambura instrument, Vidwans normally instruct the 'strummer' to skip the first string (P) so that only the Shadja will be heard for P varjya ragas. The P string peg (beradai in Tamil) was manually adjusted to 'M' only for madhyamasruthi based scales like Chenchurutti , Nadanamakriya or Punnagavarali during the Tukkada session. (as children, we in fact waited for this educative session and tuning of 'adamant' instruments often elicited interesting reactions from the vidwans!).
For ragas like Sriranjani, Abhogi, Hindolam etc.which are NOT madhyamasruti ragas, the scales appear to be rather 'hijacked' when 'M' is employed. (the ‘M shift’ is so easy nowadays with e-boxes). On being discussed, many artists have told me that keeping M sruti for P varjya ragas gives them a different 'feel'. It could be a personal preference but has become very common.
A senior vidwan once told me that yesteryear vidwans didn’t ‘touch’ the tambura once it was tuned ‘PSSS’ pitch-perfect. Skipping P or tuning to M for madhyamasruti rags could only be a later development as Prakrti swaras shall not be disturbed! Some old recordings bear testimony to this, he said.
In the Hindustani system, I have ‘seen’ tamburas tuned to Kaakali Nishada (in place of P) even for ragas not containing that note! For Hamsaanandi ( I don’t remember the H equivalent raga name) I came across a singer using G. in place of P.
While setting sruti, No M for P varjya ragas and M only for madhyamasruti ragas - that's my preference!