The GTVA has a lot more to lose then face if it withdraws from Sol. Viet Nam and WiH aren't comparable. If the American populace had spent the decades prior to Viet Nam being sold the idea that it was a 'promised land' that their government would open up for them, then it would. The GTVA, (or at least its Terran Arm) has staked its very existence on capturing Sol. Mix in that the Americans were LOSING Viet Nam, and had no right to be there. The GTVA has some thin veil of law that they have staked their war on, and their winning.. handily.
Madrid isn't comparable either. Because that is Person C being harmed by Person B in response to the actions of Person A.
Al Quaeda directly attacked the United States on 9/11, in what was a blatant massacre and war crime. Support for going over seas to bring the perpetrators to justice was ridiculously high. When a definable enemy commits and atrocity against you, it ups the motivation to get vengeance. It only lowers support for vengeance when the victim is just collateral of other people's conflict.
Case in point, the GEF's may view the GTVA's incursion positively, but if the UEF military were to start cruising around the Kuiper belt (i know they don't have the assets for it, but just a what if) destroying GEF bases and colonies, support for the Tevs among the GEFs would drop dramatically, as the Tev incursion would be increasing Ubuntu militarism and spilling over onto the GEF's.