Excerpt from email from R Eitan Feiner “Even one who typically follows Rav Yehuda HaChassid’s instruction to avoid shaving/haircuts on Rosh Chodesh, according to several Poskim (Rav Moshe Feinstein; Rav Y. S. Elyashiv), he may indeed shave when Rosh Chodesh I’yar coincides with Erev Shabbos.”
Additionally my own 2 sense. I did a quick check on calendar it seems whenever rosh chodesh Iyar is on Shabbos, Friday Is also rosh chodesh (at least in our set calendar) and the M”B is talking about rosh chodesh Iyar when he says it’s muttar to shave/haircut. So it seems we have the M”B also that’s allowing shave/haircut on Rosh Chodesh (at least when its Lkovod Shabbos and Rosh chodesh) (maybe he’s even allowing shave/haircut on Rosh Chodesh lekovod shabbos throughout the year even when shabbos is not Rosh Chodesh).