Can I safely use antiperspirants containing aluminium?

Yes, applying antiperspirants to healthy skin is perfectly safe.

EU Statement via the BfR: Absorption of aluminium through the skin is unlikely

2014 The German Federal Institute for Risk Assessment (BfR) conducted a health risk assessment of aluminium-based antiperspirants in 2014. At the time, the available data was contradictory. Consequently, the Institute highlighted a need for further research. The industry was requested to measure aluminium absorption through the skin. A task that proved extremely challenging and required significant resources to complete.
2020 On 20 July 2020, the BfR published its final conclusion for the entire European Union, confirming that no aluminium are absorbed through the skin. They stated: "Health impairments caused by the absorption of aluminium through the skin are unlikely." You can read the full BfR Opinion 030/2020 of 20 July 2020 here.
2023 This safety assessment was further confirmed and solidified at EU level by the Scientific Committee on Consumer Safety (SCCS) (Opinion 045/2023). View the SCCS Opinion 045/2023 here.

In summary: when applied correctly to healthy skin (avoiding freshly shaved skin), the use of these products is entirely safe.