I go to a Shiur in a Shul and noticed two women nursing their babies in the Shul in front of the Aron Hakodesh of course they cover themselves, but I was wondering if this is permitted due to the Kedusha of the Bais Hamikdash Me'at?
Nursing in the presence of women only - during which the nursing mother covers herself - does not intrinsically violate the sanctity of the Bet Knesset. It could, however, effect the decorum in the shul (even bringing infants to shul who are not nursing could interfere with decorum), disrupting the kavanot of those women who are praying. For this reason the rabbi of the shul, who is aware of the nature of the commmunity, should be consulted and his psak followed. Based on prevailing social norms, if men are present or could enter the room, it would be immodest to nurse even if the woman covered herself.