When will it be possible for the Librem 5 to run android apps?

Anbox, like WINE isn’t perfect. It can run apps, but there will be compatibility problems.

As for NewPipe. There is a bigger issue. We need hardware video decoding to get any reasonable performance out of a video player (Unless you can tolerate with very short battery time with CPU decoding). And it seems that it won’t happen soon. The Etnaviv devs have just started to get NIR (a Mesa internal stuff) working. They are far from reverse engineering the video decoder and making it work on Linux.
With that said. If the NIR developing goes well and they manage to get OpenCL working on Etnaviv. We might be able to decode video using the GPU. Yet it’s still way more power hungry than the hardware decoder.

Dual booting a AOSP system might be a solution. Hopefully someone will release multirom or GRUB for Librem 5.