There's no blanket Italian law requiring taxis to accept pets — it comes down to individual driver discretion, and results can vary even within the same city. Many drivers accept small pets in a carrier without issue, but it's courteous — and practical — to ask before booking rather than surprising the driver at pickup. Mentioning the pet upfront, 'con cane' ('with a dog') as a note in an app booking or said directly over the phone, avoids an awkward moment at the curb.
Uber in Italy operates mainly in larger cities and functions somewhat differently from its US model, working more like a licensed car service than a peer-to-peer rideshare. Confirming pet policy at the time of booking is the safest approach either way.