I have familiarity with Hindu Temples so I will be able articulate my views using them as a basis. However, the debate is also about restrictions placed on women at some Dargahs and Mosques too.
I write this article in the background of a lady in Maharashtra, Ms. Trupti Desai starting a high profile campaign for temples to permit entry of women into the Sanctum Santorum, particularly of the Shani Shingnapur Temple near Ahmednagar. Once she raised this issue, similar voices were heard protesting the barring of the entry of all women from age 10 to 50 at Sabarimala in Kerala and the restrictions placed on woman entering the Haji Ali Dargah at Mumbai. Please see link below:
In my experience, it is only in Maharashtra that one has seen this practice of all devotees getting access to the Sanctum Santorum and making offerings to the presiding deity, and hence the demand is quite an explosive one elsewhere. In most other temples, definitely in the Southern States, nobody except the designated priests are permitted to enter as they have to maintain a certain decorum (much like Surgeons preparing to enter the OT, like bathing, wearing fresh sun-dried dothies, observing certain religious practices at home, etc.) and nobody else is allowed to enter.
As everywhere, some rules are broken in some temples for VIP visitors which is an abhorrent practice and must be stopped.
Thus, if all temples bar the entry into the Sanctum Santorum for ALL people other than the presiding priests and have no restriction at all on anybody else entering the public spaces of the temple to pray, it should be seen as an enabling and egalitarian solution to the problem.
Some temples bar women, some bar men, some bar non-Hindus etc. which should be viewed as being anti Constitutional and such restrictions must be banned by law, to the extent that everyone regardless of caste, creed, race or religion shall have free access to the 'public' spaces in a temple.
When it comes to women, it must be said that they are the most mature ones in any society and are the true keepers of tradition and faith. Thus, if they feel uncomfortable entering a place of worship on certain days, (I see this in my family) they will not enter. Others may feel that they have a right to enter regardless - and it is our duty to protect that right, but to ensure that religious sensibilities are not unnecessarily trampled upon, restrict that right to the 'public' spaces of temples.
Thus, to sum up: Open the doors, but restrict entry to the OT to only the Doctors and leave the choice of entry (or not) to the public spaces of a temple to the devotees.