Here is an interesting halachic discussion that one could say is fairly new...

The Israeli government created a new section along the Kotel for egalitarian prayer. Some people have found that this is a nice quiet place to pray, and much of the time it is fairly empty. Some people have held family get-togethers and simchas in this "azarat yisrael" section, others just go there to pray privately and on their own, while occasionally a small group might forma  minyan in this quiet section.

Someone sent a question to Rav Asher Weiss asking if a religious person is allowed to pray there, since it is designated for prayer services to be held by Women of the Wall..

Rav Weiss's answer is to consider this place like any other Reform synagogue. Rav Weiss said that the gedolei hador have already prohibited, for a few reasons, for a frum Jew to go and pray in shuls of those organizations. One must stay far away from them, as they are disbelievers, and one is not even allowed to rent a room in their buildings to be used for making a minyan.

Even, Rav Weiss continues, if there is no issue of "maris ayin" - if it becomes public knowledge all around town that there is a private haredi minyan there, it would still not be allowed.

After trying to suggest possible justifications, Rav Weiss concludes by sticking to his guns that it is prohibited for a frum Jew to pray in the azarat yisrael. One must stay away from that area, as it is clear that they will use it in their propaganda showing how many people use the area under their control. One cannot do anything that can be used in a way that will strengthen them.

Rav Weiss concludes by adding that one should do everything in his power to put an end to this program of them controlling this area, as it is a desecration of the holiness of the place from where the shchina never left.
(Source: Kikar)