The issue of creating an EU Army command is dividing the nationalists of Europe. On the one hand it affords an opportunity to break free of NATO and US dominance, or more properly can initiate a process toward that end. No one is suggesting that NATO is going to just go away. It is already becoming apparent through the Trump's cabinet picks that an Anti-NATO or Anti-Atlanticist doctrine is not going to govern his administration.
Nevertheless, the leaders of Germany, France and even figures like Hungary's Viktor Orban are calling for an independent EU command. The European Right has long wished to be free of the US and the Trump victory combined with Brexit have afforded a unique opportunity.
On the other hand, we see the Austrian Establishment which though not part of NATO understands the way in which historical forces reassert themselves. An EU command will effectively mean a surrender to German leadership. The Austrians have a long uncomfortable history with German dominance going all the way back to Bismarck and German unification. It led to the dissolution of their empire and finally the subjugation under Hitler in the form of the Anschluss. While a Hitlerian Germany is not on the horizon, the EU was not created to reestablish Berlin as the master of Europe. German reunification restarted this impulse and not thirty years later it is once more on the horizon.
This question is further complicated by the Austrian Right's position vis-à-vis Germany. While Pan-Germanism was at one time embraced there's been shift to a more restricted Austrian Nationalist position since the 1980s. In addition, some would view an EU army as being not so much Berlin dominated but as Brussels dominated, to which they are very hostile. It depends on one's read and understanding of power within the EU framework.
Austrian Nationalism has vacillated on the question of neutrality. There were calls in the 1990s to join NATO. Instead it opted for the 2nd Tier Partnership for Peace (PfP) an option that allows nations to work with NATO but avoid an integrated command. Despite refusing to fully join NATO, it was clear a new European Order was being created and Vienna decided to join the EU in 1995.
While Neutralism is still desired by elements within the Austrian Establishment, they more or less vacated the position in the 1990s by these European integrations. Twenty years later they are having to reckon with the costs and consequences of the EU project and the ways in which it has both failed and transformed society. The Austrian Right may try to pull out of the EU and perhaps even the PfP, but it is doubtful that either Berlin or Washington would allow such an insurgency within the continent itself. But with a Trump administration in the White House, who knows? One thing can be sure, the leadership in Vienna will be very careful in considering leaving the question open to plebiscite. In this era of renascent populism, such a move is potentially perilous.