Can someone in a distant community include people converted to judaism under conservative or reform into a minyan, due to the difficulty to find bona fide Jews? I would say no, but my chavrusa says yes. Yasher koach.
Somebody converted under the Reform or Conservative movements would not be able to join a minyan.
Sources: There are two element of a conversion that are problematic under Reform or Conservative. One is that a conversion requires a beis din, and people who do not fulfill mitzvos, and publicly desecrate Shabbos, are disqualified to function as dayanim on a beis din. The other is that conversion requires the acceptance of mitzvos, which is not properly done in Reform or Conservative conversions.
Rav Moshe Feinstein, in discussing a Conservative conversion (Yoreh De’ah 1:160), writes that there might be room to validate (post factum) the acceptance of mitzvos, but that the conversion is not valid because of the lack of a qualified beis din. If the Conservative conversion was done with a beis din of Torah-observant Jews (which is unlikely, to my understanding of the movement), then the Conservative convert would be able to join the minyan.