I know people don't think the Deform and Conservative synagogues are not real synagogues, but they certainly are not temples. In Judaism, only The Temple in Jerusalem is called a temple. It is forbidden to have a temple or even bamot outside of The Temple Mount.
Even the Bolshevik media is not calling it a temple. Also, in contrast to most Deform and Conservative synagogues, this synagogue doesn't even have temple in its name. Many Deform and Conservative synagogues call themselves "Temple ____" rather than "Congregation ____". This one calls itself Synagogue in the name, not even Congregation.
I get offended when people say temple rather than synagogue or "what temple do you go to?". I would say I don't go to any temple. I go to synagogue.
The shooter doesn't differentiate between Liberal Jews and Orthodox Jew. They were killed Al Kiddush Hashem for being Jews.