Is it permissible to take a haircut prior to davening Mincha, even late in the day, unlike what it says in the Mishna and Shulchan Aruch?
There are sources that say that nowadays that haircuts do not take long at all, it would be similar to the opinion that it is permitted to eating a small meal near mincha katana. However it is only said as a limud zechus, but not as something that should be done l’chatchila. Others say that if the barber has two or three pairs of scissors, (or haircutting machine) then we don’t have to fear that if one breaks that he will have to look for another one, which will take a long time. Although this idea is controversial, one may rely on this opinion.
Kitzos Hashulchan 26 ftnt. 15, M:B 232-6, Shar Hatzion ibid. 3, Ben Ish Chai Vayakel 1-11.