There are multiple reasons:
There are not many countries in the world today, citizens of which would be willing to massively demonstrate for Western democratic arrangement in their home countries. We should thus definitely appreciate that and show support.
If the demonstratos fail, they may see migrating to West as the next best alternative for themselves. I guess you don’t want to see yet other millions of migrants in Germany, do you?!
Remember that those who organized resistence against communist rule during the communist times in East Germany also found moral support and ingerence of West as more encouraging for their further effort than it might have seemed from the external viewpoint.
You may be surprised but at the moment the (banks of) “Eurocommunity” live at the expense of Czechs. The reason is that ECB still has negative interest rates (which means that Eurozone commercial banks would have to pay money if they want to store money in ECB) but the Czech National Bank has gradually increased their interest to 2% p.a. during this year (which means that it pays this interest rates to commercial banks that save money in CNB). That’s why many big Eurozone banks (especially those that also own banks in the Czech Republic (e.g. Belgian KBC, French Societe Generale, Austrian Erste, Austrian Raiffeisen, Italian Unicredit, Dutch ING, etc.) virtually transfer huge sums from their branches in Eurozone countries to their Czech branches that than save this money in CNB and thus get 2% p.a. basically for nothing. And we are talking huge sums - billions or even trillions of Euros, way beyond the real economy. See the article here: https://www.e15.cz/byznys/finance-a-bankovnictvi/zahranicni-matky-bank-vydelavaji-na-politice-ceske-narodni-banky-1361215
For this reason, I do support to have a single currency in EU because it can prevent such speculations that can lead to huge profits of speculators without any effort. Of course, it requires reasonable fiscal rules (and mechanisms to ensure that they are respected by all the players) and reasonable monetary policies of ECB. It was German mistake that you exchanged the role of future ECB governor for the role of the EC president. Considering how much ECB policies affect economy, it may be even more important role than the EC president whose powers are limited by EP and decisions of national states.
In general, I think it is more important to focus on the performance and efficiency of the real economy rather than the virtual accounting operations - money should only facilitate the trade after all, not to be the value per se. In this respect, EU is falling behind the progressive countries in the world today and needs to accelerate its development (both as together as the single economic space as well as national and regional efforts). This is thus very important goal especially for countries that have been declining in recent decades - and Italy belongs to one of those. I’m not sure whether the 5-star Movement government will do any better reforms than Salvini’s League that has base in relatively prosperous north of Italy and more understands what it takes to achieve and maintain prosperity.