This depends on the equipment.
Setting aside synchronous machines like induction motors that are affected by line frequency, you have to consider the earthing + neutral arrangement in the appliance.
EU standards have the following classes:
- Class O - 2-wire plug, not double insulated
Not safe on split-phase. Class O devices only have a single layer of insulation between exposed metal parts and line voltage. If there is a device fault and it's on a split-phase system, the exposed portion will be at 120V or 120V, vs. 240 or 0V if it were on its native EU system.
Even worse, devices that have exposed lamp socket bases that are supposed to be neutral (like the lamp bases of old-school Christmas lights) will always be live when connected to a North American split-phase feed.
- Class I - 3-wire plug with protective earth
These 3-wire appliances are safe on split-phase 120 if there are no exposed neutral points. Again, if it's a lamp with a screw base, nope - the base will be at 120V, not neutral.
Something to verify however: ensure there is no bond between the 240V appliance's neutral and protective earth before hooking it up. I can't vouch 100% for this not being a thing in the EU (I don't believe it is). A 240V appliance sourced from outside of the EU? I’d have no confidence of this unless I were to check it myself with a meter.
What makes me paranoid about this issue is the fact that some North American 120/240V appliances (e.g., clothes dryers) allow bonding neutral to protective ground in the appliance, to be able to use the old 3-wire L5-30R ‘dryer’ plug.
- Class II - Double Insulated (no protective earth)
These 2-wire appliances are safe on split-phase, as there is no exposed line or neutral, and in addition have an extra layer of reinforced insulation to protect against faults. Most devices with plastic cases are like these, such as phone chargers.
- Class III - SELV Isolated
These 2- or 3-wire appliances are safe on split-phase. SELV devices are powered by isolated supplies, that is, with no galvanic connection to the primary at all, and stringent limits on primary-to-secondary leakage.
Two things to be wary of in 240V land.
First, be suspicious of 240V appliances originating outside of the EU. Many lack a proper CE (let alone TüV) rating. Watch for the ones with the 'China Export' fake-CE marking. More here: https://www.cemarkingassociation.co.uk/ce-marking-and-the-chinese-export-logo/) If you're buying something off Alibaba or Temu, beware.
Second, when using North American split-phase, both 120V legs will have breakers, vs. only the 'hot' lead on a 240V EU-style plug. The 120V breakers are usually tandem but might be separate. In the unlikely event they are separate, it's possible that a device could fault line-ground on one leg, leaving the other leg still live with just the one breaker tripped. This wouldn't happen on an EU system, which would disconnect the 'live' leg, leaving only neutral connected.