All of the Gedolim strictly forbade going up to Har Habayis - Rav Elyashiv, Rav Valdenberg, Rav Ovadiah etc. etc. etc. Here is a video of the former Chief Rabbi, Rosh Yeshivat Merkaz HaRav, Rav Avraham Shapira. He was a true gadol bi-yisrael.
Two reasons not to go up. 1] It is a safek kares. 2] The Gedolim forbade it.
I am so surprised that rabbonim who would themselves admit that there are not in the league of the אוסרים insist on encouraging it. [I would link a sign encouraging people to go up with all of their names affixed to it but I don't think it would be in good taste.....:-)].