It really depends on the travel adapter(s)
Stacking two of them isn't really the issue. It's that an awful lot of that stock is made in the far east, and lacks any certification by any competent testing lab. (in fact the CE mark can be counted on to be counterfeit unless an EU bricks-and-mortar manufacturer made or imported it).
So look for ones with the stamp of a reputable testing lab. These shops don't bury the lede: If they have a hard-won UL Listing, ETL, BSI, CSA, TUV etc. -- they'll put it front and center. However if the most prominent mark is CE or CCC, that means they couldn't get a proper listing; it's a self-admission of junkness.
It also depends on the load, in two axes.
Is the load double insulated?
If you see a "Square on Square" symbol (literally a square inside a square), that means your load is double-insulated. That will help compensate for adapter problems; not least that these adapters love to exchange hot and neutral. [not least, British BS1363 (Type G) puts hot on the left (ground down), US NEMA 5 (Type B) puts it on the right.]
Is the load small?
Adapters are notorious for very flimsy connections. You can get away with murder if your load is only a 10 watt iPad charger. But trying a 1500 watt hair dryer is asking for trouble. The issue is "series arcing faults", where the power jumps (arcs) across a flimsy connection in order to get through your device. The more current, the more arcing; shut off the load and arcing stops. An arc-fault detecting circuit breaker will help protect you, but those are rare.
Is the outlet GFCI/RCD protected?
A GFCI aka RCD/RCBO device will help keep you from getting shocked by a loose or broken adapter. It won't do anything to prevent arc-caused fires, the aforementioned arc-fault breaker (AFCI) would do that.
Either protection could be located anywhere in the building; the proof of the pudding is if you hit its TEST button, the outlet loses power. It's generally at the receptacle itself, or at a nearby receptacle, or at the circuit breaker; all are equally acceptable.