they are all tempered.

Stability is not the issue but cleaning sure is but if fluting is only on one side then face that out not in the shower for sure and yes all are tempered

Yes, fluting is on the outside - not sure if keeping the outside clean would be an issue.

Why fluted......rather a dated feel and shrinks the look of the bath : ( with a more closed in feel.)

Glass is not the weak point, the quality of the door and frame is the issue. Also why a fluted glass as it will be much tougher to clean.

Of course keeping the outside clean will be an issue everything in a space needs cleaning . I have pixelated glass entry doors on all the rooms off a long hallway including a bathoom they get cleaned pretty much every week just like everything else .

You could consider the "rain glass" pattern instead. Ten or twenty years of weekly cleaning means extra time spent on cleaning fluted glass is a lot.