In case you are still having trouble with the issue, in short, yes, Shopify will automate the VAT costs, but you first have to set it up correctly for each country in your tax settings.
I googled around a bit and found a guide to setting up VAT for Shopify stores in the EU. There are also a few other articles that will help you setup everything.
However, settings up VAT isn't so much of a problem as having legally-compliant invoices in my opinion, as this has to be a valid document for the accounting legislation.
I'm testing Sufio automated invoices for Shopify in my store for a few months now. It's pretty good, you don't have to worry about tax problems anymore.
Hope this helps!
Ashley provided some great links and she's right; if you setup your tax settings correct (in your case setting all EU countries to 25% VAT and all other countries to 0%) Shopify will automatically apply the correct VAT setting to your customers order.
I'd also ike to poiunt out an interesting app we developed called Digital Takeout: Multiple Pricing. It allows you to list the VAT included and VAT excluded price so it's clear from the start what your customer pays. You can try it for free here.
Hope this helps and good luck!
Shopify will collect consumption taxes for you, but you must configure your store to do so. Have you consider to use a compatible software solution to automate the sales tax mess?
Quaderno validates VAT numbers, issues tax complying invoices, automatically updates the sales rates when they change and notifies users every time they surpass a sale threshold. Also, with Quaderno tax reports, tax filing is a matter of minutes not hours.
Disclaimer: I work at Quaderno. If you have any questions, please feel free t reach out. I'm happy to help.