There is a halachik principle brought down in the Talmud and codified in halacha known as shaat hashmad - a time of forced religious persecution. Generally, the rule is that any commandment of the Torah does not demand martyrdom for its observance with the exception of the 3 severe sins (idolatry, sexual crimes [i.e. adultery, incest, homosexuality, and bestiality], and murder) and the desecration of G-d's name (see Rambam Hilchot Yesodei Hatorah 5:2). However, at a time when there is a movement on the part of the non-Jewish authorities to destroy Jewish practices, then even minor commandments (or even mere customs) also demand martyrdom for their observance (see e.g. Rambam Yesodei HaTorah 5:3).
Recently, Arab leaders have successfully incited Arab terrorists to commit violence against Jews with a short term aim of preventing Jewish prayer in the Old City (e.g. atop the Temple Mount or at its Western Wall) and a continuing long term aim of exterminating/expelling the Jews from Israel. In response, some Jewish religious leaders have advocated that Jews avoid entering the Old City until the situation calms down. Considering that the threatened violence is intended to prevent Jewish religious practices, why shouldn't maintaining these practices (i.e. praying/visting Jewish holy sites) fall under the spirit/letter of the shaas hashmad law indicating a need to involve some level of mesiras nefesh?