The custom of going to the Kotel, the “Western Wall,” isn't exactly the ancient custom everyone might think it is.
Remember, going up to Jerusalem to bring sacrifices for the holiday meant Although there are those who would like you to believe it is the same thing, it isn't,...far from it. The Kotel is not a part of the Miqdash (The Temple); it is part of the current retaining wall, as it were, of Har HaBayith (Temple Mount).
This custom of visiting the Kotel on Hag HaShavu'oth, interestingly enough, started one week after the day we now celebrate as Yom Yerushalayim.
Religious Jews from across the spectrum took the opportunity staring them in the face, to come as close as the could, or as close as they dared, to Har HaBayith.
Satmar Hassidim make up at least one group of Jews which avoid the Kotel, in order that it should not become the focus for avodah zarah. I have not too many people moving in this direction. Yet, they have a fair point. After, our focus should be on Har HaBayith.
This is also increasingly, albeit gradually, becoming the custom of a segment of the Religious Zionist community, among others, which has woken up to this misdirected focus, and are doing their best to correct it, by raising awarenes, ascending Har HaBayit in the proper manner (ie. kosher immersion, no leather, etc.), and encouraging others to do the same.
However, there are those who believe we should continue to frequent the Kotel area, if for no other reason than to combat the increasing Christian presence there, as well as in the nearby City of David. This certainly makes for a compelling argument.
In any event, let us never lose sight of what is behind the Kotel, and becoming increasingly more accessible to Jews. We must maintain and do what we can to increase that access, eventually retake control of it, and see the Hillul HaShem wiped out!
Below is a clip of Rabbi Moshe Dovid Tendler on Har HaBayit, accompanied by Rabbi Tovia Singer (courtesy of Kumah.org), followed by some additional resources. The full version can easily be found on YouTube.com. If you don't accept other rabbi's opinions of the acceptibility of ascending Har HaBayit, then perhaps you will accept Rabbi Tendler's.
Temple Mount Resources:
Temple Mount Institute, Rav Yisra'el Ariel
Temple Mount Information Center, Rav Tsvi Rogin