My hairdresser is male, I am never the only person in the shop, is this problematic?
It does not appear that there is any prohibition for a lady to go to a male, non-Jewish hairdresser.
Having said all of this, it remains a virtue to go to a female hairdresser, in particular for married ladies.
Halichos Bas Yisrael (p. 95) cites from Rav Chaim P. Scheinberg that me’ikar hadinthere is no prohibition for a lady to go even to a Jewish male hairdresser.
Based on Shach (195:20) and Pleisi (195:7), he explains that because the hairdresser is occupied with his job, there is no concern (me’ikar hadin) for hirhur (forbidden thoughts). Other opinions do not concur with this, and write that the occupation of the hairdresser with hair cannot be compared to the occupation of a doctor with a patient, because the entire purpose of the occupation is to beautify his charge. See, at length, Netzach Yosef, Vol. 1, no. 66, and see an interesting correspondance on the subject (Hebrew) here.
The debate above is said specifically with regard to a Jewish male hairdresser, who is obligated to avoid any hirhur, and who is liable to transgress the prohibition ofvelo tasuru acharei… eineichem. For a non-Jewish hairdresser, however, this does not apply, and therefore there would not be any prohibition, even according to the authorities who are stringent for a Jewish hairdresser.
The ruling of the Rambam that you mention (Issurei Biah 21:1), who writes that for arayos a Torah prohibition applies even to forms of physical contact other than actual relations, such as hugging and kissing, is not relevant. It is everyday practice in the world for ladies to go to male hairdressers they don’t even know, and this is clearly not a form of maga chibah, an ‘intimate touch’ (like a kiss) that is forbidden.