The first thing the invading Israli forces hits is a mosque.

That is all that needs to be said.

It's not like PIJ has designated military bases set well aside from the civilian populace.

Israel has litle clue about operations of Hamas and was thus completely surprised by the attacks.

Israel is well informed about Hamas operations and thus is able to precisely target their hideouts.

Pick one as they can't obviously be true at the same time...

I've add that this would not be remotely out of line with history. Weapons have been stored at Al-Aqsa even in the past.

https://www.haaretz.com/israel-news/2017-07-20/ty-article/watch-how-assailants-carried-out-temple-mount-attack/0000017f-f595-d460-afff-fff70d7a0000

If there were actually weapons hidden there, it's a valid target.

Still, blowing up hospitals, religious buildings, and schools is generally a bad idea. Even the US thinks twice about it (before hitting it with a drone strike).