Always wanted to know, but was too afraid to ask

Assume we have two MH lamps, one is Rx7s, other is G12 type. Both have the same symmetrical burner, the same tube diameter. But Rx7s one is listed for horizontal +- 45 degrees burning position, and G12 is listed as universal 180. Any physical reason behind this? Or is it just a 'tradition'? )

I’d say tradition?, you wouldn’t assume Rx7 to be run vertically but to the discharge tube it probably wouldn’t make any difference as the zinc oxide white end coating is applied anyway?
Interestingly though, all the lamp catalogues and guides I’ve read over the years state slightly higher lumen output and better performance when running vertically?

Overheating of components the lamp and/or lanterns are not designed for:
Socket (the one on the top) not rated for the temperature it may reach when Rx7s burned vertically
Seal construction, designed to never be on the top, the one on the bottom running too cold and suffer from liquid fill exposure it may not be designed to handle.

The fact the burners look similar and even could be made using the same components does not necessary mean they are the same. There may be differences in the fill sand used to fill the space around the lead wires in the seal tubes (assume CMH here), there even may be differences in exact dimensions of those arctube parts, optimizing the performance when the use won't expose them to the aggressive (towards the PCA material) fill salt condensate so won't need to resist that condition.

Well, here we have three 150W quartz MH lamps in 'Venture' style. All three burners are essentially the same. The one on the top just lacks zirconia white coating because it is a color lamp. The one on the bottom has some unfused quartz tubes at the ends, but this does not mean much, just some minor technological nuances.

Also you can see, pinch styles on the external bulb are essentially the same too - just obviously, G12 lamp runs two foils leads.

Regarding visually identical, but technologically different burners in use - just anyone related to the mass production, myself including, can confirm that unnecessary nomenclature is avoided like plague! Even slightly higher costs are usually tolerated in the name of parts unification.

Having as much as possible production unified is indeed exceptionally strong argument why even tolerate a bit worse performance or even a bit of extra material cost, however
in the picture I see there lamps with three visually different seal assembly designs. And not counting the lack of the white coating on the top one.
Botom one has tube overhang over the lead in wires, the center one has them significantly shorter, the top one has different dimmensions of the Moly seal foil.
So there the motivation for the differences was still really stronger than the need to unify production.

Otherwise why won't all of them use e.g. the shortest arctube design (so it could be usable within all those three lamp formats).

And even when the arctube would be the same (as I would expect at least some makers will go for at least for some lamp formats), there is still the socket temperature loading problem or the general mechanical assembly (and its impact on e.g. failure mode safety), which means regardless of the arctube performance, may restrict the operating position.

The question still remains unanswered...

For tungsten halogen lamps which share the same sockets design, vertical operation is out of question, sure. But they (1) have gas fill which will screw up because of internal convection and segregation if run vertrically, also making upper end very hot, and (2) MUCH higher thermal load than comparable sized MH lamps. About a magnitude higher!

MH lamps in RX7s do not have gas filled external bulbs typically, and outer diameter is much larger. So no internal convection in outer bulb and much weaker external heat flow.  I do not believe that upper end will overheat significantly, and more than a base of G12 lamp when run base-up.

So I still believe this limitation is mostly a carry-over from linear tungsten lamps. Exactly just like a popular belief that touching a quartz external bulb of MH lamp with bare hands will destroy it (it will NOT, confirmed by a manufacturer's manual). Just because again it runs significantly cooler than a surface of tungsten halogen lamp.