What kind of tubing should I use for draining condensate from a furnace / boiler?
TLDR: Plastic tubing seems the safest to use. You may be able to use certain types of metal in some cases, but acidity in the condensate can damage those materials.

ICC model building code as an example says the following (in part):

SECTION 314 - CONDENSATE DISPOSAL
[M] 314.1 Fuel-burning appliances. Liquid combustion byproducts of condensing appliances shall be collected and discharged to an approved
plumbing fixture or disposal area in accordance with the
manufacturer’s installation instructions.
Condensate piping shall be of approved corrosion-resistant
material and shall not be smaller than the drain connection on the
appliance.
Such piping shall maintain a minimum horizontal slope in the direction
of discharge of not less than 1/8 unit vertical in 12 units horizontal
(1-percent slope).
[M] 314.2.2 Drain pipe materials and sizes. Components of the condensate disposal system shall be cast iron, galvanized steel,
copper, cross-linked polyethylene, polybutylene, polyethylene, ABS,
CPVC, or PVC pipe or tubing. All components shall be selected for
the pressure and temperature rating of the installation.
Condensate waste and drain line size shall not be less than 3/4-inch
(19 mm) internal diameter and shall not decrease in size from the
drain pan connection to the place of condensate disposal.


However Inspectapedia has some additional information on this topic which seems more cautious:

Condensate from condensing boilers is quite corrosive... That's why
plastic is a good drain material. Stainless steel might be acceptable
in some situations. I'd be careful about using brass, iron, copper,
galvanized pipe.

[Those materials would be sensitive to acid and could be gradually eaten away]

It seems that cases where you can use metal are when the condensate is diluted to a level which won't cause a problem. For instance, when it is introduced into a sewage line which is regularly used for other purposes. However, copper, brass, and related metals seem like a bad idea even in those situations.
This was described clearly in a Green Building Advisor post:

Don't sweat the acidity of the condensate going into the septic tank.
The volume is low (relative to daily drain flows...) and of things go down the drain that are at least as acidic as
natural gas or propane condensate. It's strong enough to react over
time with copper drains, but with iron, not so much.
The lower the pH, the more acid the solution is. Even the most-acid
gas-burner condensate has a pH no lower than 3, most are between 3-5.
Dry wine has a pH of about 3.3 (about the same as orange juice), even
sweet wine still under 4, typical soft drinks are between 2.5-3.5,
cranberry juice is between 2.0-2.5.
[In cases where the condensate will be diluted it would be a mistake to use]
copper, which is far more reactive to acids than iron/steel.
Brass/bronze and other alloys of copper will have the same issues when
chronically exposed to condensate. With drains down stream of a
dilution point such as the laundry sink hardly matter what the
material is, since in a typical applications there is many times
greater flow of the washer outflow as there would be from a condensing
natural gas or propane burner mixing in with it.