I have finally found a suitable case without glue, without magnets, but with hidden rear cameras! 
I had already been interested in this product range with the size 3XL (5.9 - 6.3"), but I found out:
But who would have thought that this cover would have been too big anyway? Even though the FP4 has a 6.3" display! Incredibly, you have to take Hama Booklet "Smart Move", size XXL (5.2 - 5.8"). The description says: for smartphones with a maximum size of 8 x 16 cm. I have measured the case. Its outer dimensions are: width x height x thickness = 8.8 x 17 x 2 cm. This size fits perfectly. Slightly larger than the FP4, but not too large. You can buy it on Amazon, Ebay, … But here is a link from the manufacturer where you have an overview of all model variants:
.Suchergebnis: booklet smart move xxl | Hama DE
The cover is available in different colours and surfaces. But beware! I bought “Smart Move” and it fits. “Smart Move - Metallic” I tried and it doesn’t fit!!! It is a bit smaller!!! So I assume that “Smart Move - Rainbow” will not fit either. But probably “Smart Move - Carbon” will. So all in all, this product range is very confusing in terms of sizes.
All connections and buttons are completely free, except for the power button. This is covered by about 4 mm when the smartphone is positioned in the centre of the case. Switching it on still works without any problems.
I don’t know if the fingerprint sensor also works this way. It would probably not be advisable to position the smartphone flush at the top. Then the power button would be completely free. If necessary, you could always push the phone up a little and then back again. But won’t that get on your nerves at some point? If you need the fingerprint sensor, you should first try out whether the upper part is enough for it.
The clamp is stable and holds the smartphone firmly and securely. It reliably stays in the position in which you have turned it. When the smartphone is turned 90°, the cameras are completely free.