Does tilting the bike on a repair stand so the fork is vertical impede any repairs? After you've experimented with various rotations of the bike on a stand, which position do you end up using?

I initially thought that the logical position is to align the wheels so they're at equal distances from the ground.



That doesn't work so well. The handlebar will not stay put without hooking the extra support bar. (The main disadvantage of the support bar is that instead of spending a few seconds to set the bike and close a quick release, it's necessary to tinker for several times that much. If it can be avoided, at least for quick jobs, it's better.) Another factor, the bending moment applied on the seat post, may not be a cause for worry, since the bike itself is so much lighter than the rider on the seat.

In any case, it's pointless to make the bike look like it's about to fly. It's perhaps more sensible to keep the seat post (and we should be hanging it from the seatpost to avoid crushing the frame) vertical, as in the second diagram above.

Now even in that position the handlebar could tilt.

Do you tilt a bike on the stand all the way until the fork, not just the seat post, is vertical?

Update (after Henry A. Kissinger's comment)

Another way of asking this is: Does tilting the bike until either the seatpost or the fork is vertical impede any repairs? Is there any advantage to keeping the bike level?
How your bike is positioned in a work stand should depend on the type of work you are going to perform.

Much of the time it seems more convenient to have the bike in the stand so it is titled forward with the front wheel a fair bit lower than the rear. Such as position prevents the front wheel from flopping over and puts many key components and systems such as both derailleurs, the rear brake, front crankset, handlebars and shifters at a good working height in relationship with each other.

This minimizes the amount of excessive bending and reaching required for many common tasks such as adjusting shifting, cleaning the drivetrain, replacing chains, wrapping handlebars etc.

If you are working on a less common task such as bleeding hydraulic brakes, replacing a bottom bracket, or installing a new bash guard on the down tube of a mountain bike; adjust the bike stand height and/or tilt appropriately to accommodate the specific task you need to perform. 

For something like bleeding a rear hydraulic brake this could mean lowering the overall height of the stand and rotating so the the front of the bike is tilted higher than the rear wheel to maintain an upward flow from the caliper to the brake levers. 

It can help to have the bike level when adjusting the saddle’s angle and setback but honestly it is usually easier to perform those tasks with the bike flat on the ground instead of in a stand.