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OK. I see.
First of all, I would install Plex or Emby. You can't have synchronous streaming, but it's easy to get up and running so everyone can simply watch their own movies on their own devices. Remember to disable authentication on local network since you probably don't have internet.
Now for synchronous streaming, it's going to take some time to set up, if you're up for it. There is no convenient install and forget software but it's actually more simple than it seems. You just need (1) a stream server, (2) a stream client and (3) a media library interface.
(1) You can use VLC following documentation here on multiple streaming (multicast). Transcoding may be necessary as well, which VLC can be set up to do.
(2) On each tablet you need a video player on Android that can receive the stream. Depends on the protocol of the stream, but if it's RTP, which is pretty standard, I think you can find some app like this
(3) This can be a challenge if you want something fancy. Most VLC remotes only control VLC to play things locally or at most a unicast stream. I can think of 3 options:
Most simple and least fancy is sending commands to start the stream by commandline by SSH.
Or you can start the stream via a GUI by remote desktop. This requires to set up a desktop environment in your headless server and then installing VNC. Not too difficult but takes some configuring to set up a headless desktop environment.
Most complicated but fanciest would be to set up a web interface. You could use an existing interface but you need to get down and dirty and program all the buttons to tell VLC to stream and not play locally.
Note that in any case you also need a wireless router for a wireless network. Don't forget that.