(I posted in the Live Sound thread, but include that text here as well)
Ooooh, this is a very interesting question with (yet another) "it depends" answer.
First off, let's look back a little bit into history to understand a bit about how commonly used standards came into being with phantom power and splitting.
Originally, many consoles utilized transformer balanced inputs, and in some of these consoles, the primary (microphone side) was center tapped and phantom power was fed via the CT (through a resistor). Since no DC can cross between the primary and secondary, and the primary was designed so the core wouldn't saturate with the DC current, no blocking caps were required for the head amp circuitry (other than what was necessary for the circuit to function normally). The advantage of this method was common mode rejection that was purely a function of the matching of the 2 primary windings. The disadvantage is a larger core, and what happened to the input impedance of the circuit when phantom power was switched off from that channel. If it was left open, the input impedance would rise, if terminated with a resistor to ground then DC would flow the other direction when connected to another console providing phantom power (likely causing noise and reducing the available current to the mic)
Other consoles used transformers without CT's, and phantom power was fed simultaneously to each end of the primary of the transformer. Now the common mode rejection is dependent on the balance between the two resistors, and since the two resistors are not ground referenced (and are effectively in series), they impact the input impedance less if left in place (simplifying switching). In this instance, since there is no path to ground, voltage impressed on both ends of the transformer simultaneously cancel out and no current flows through the primary. Since there is no DC flowing through the primary, the core can be smaller which can lead to a higher quality audio signal (more complicated than this, but I will leave the details of the tradeoffs out). Now with this circuit, if either pin 2 or pin 3 become grounded or connected to pin 1 through a resistor (via an adapter or via a DI that does not adhere to the traditional standards) some DC current will now flow through the primary of the transformer which does not have sufficient core to support it and this may affect the audio quality.
Currently, most consoles no longer use transformers balanced inputs. The standard differential amplifier type circuit (pick one of hundreds of variations on essentially the same thing) is easy to protect against phantom power by using blocking capacitors to block phantom power that's impressed upon the 2 signal lines from entering the diff amp circuitry. The advantages of this are that there is no way for DC current to flow into the console from ANY source, 2 consoles can be connected together without damage or signal degradation (at least from this cause). The only remaining challenges come from maintaining close balancing of the impedances between the two lines, which is a little less critical these days with high rejection circuits.
So, with modern consoles using the common input amp architecture, there should be no damage problems connecting the two consoles together. The major issues that will remain, however, will be maintaining the balance, and noise caused by circulating currents between the two console's grounds. This can be corrected by lifting all of the pin 1 connections on one of the consoles (should be the one that does not intentionally supply phantom to the mics) but it should be noted that lifting pin 1 in this instance will not remove phantom power because both consoles are ground referenced through the power source's protective grounding system.
Diodes won't work, because you would block 1/2 of your audio (positive going) too!!!
Where one major issue remains, is interconnecting equipment that uses different input topologies (such as transformerless with transformer) as currents can flow in unexpected ways causing noise . It doesn't take much DC (modulated by God knows what noise) flowing in the primary of a mic input circuit, multiplied by the gain of the head amp, to be a real world problem.
The one way that's guaranteed to isolate is by using a splitter snake, each channel has one direct path (console that supplies phantom connects to this) and one or more transformer isolated split paths that do not use CT's. Often they will use additional shielding to prevent high frequency noise such as RF from crossing the core isolation, but these are generally designed to be quite robust and can solve problems that can not be solved any other way. This is how many of the real pro applications are configured, and one that I would recommend where you will be connecting to different gear every night. My last splitter snake (32x8) cost me close to $5000 including the rack. It's not a cheap solution, but a very effective one that my clients gladly paid for.
Since I am not familiar with the input circuits used by every console manufacturer, I suggest that you take this as a general informational description of how things work as there may still be cases where it doesn't apply 100%.
Hope this helps.