Italian here, the reason behind this is that Italy is full of small enterprises, mon and pop shops, ... and until the end of the '90s tax evasion was so rampant that those shops and small companies have basically never paid a single lira in taxes. The people owning those shops are a core block behind the Italian right.

Shopkeepers in Italy are accustomed to dodging a certain percentage of VAT, and it all depends on people having cash at hand. When a society goes cashless, it's often a snowballing process, where people use cards more, and then withdraw less, so they have less cash at hand, and so on.

If people stop carrying cash with them, it will become impossible for them to refuse card payments, and thus dodging VAT would become impossible.