Technically, smart plugs are just as safe as any other device that you plug into an electrical outlet. Unless you overburden the outlet, you will not face any safety issues.
Many buyers worry about the hacking vulnerability of smart plugs. If someone manages to hack these, they could easily access other devices too. And this is particularly true if you connected these to the central cloud or hub of your smart home. Thus, causing massive damage.
Although this was a valid concern back in the early days, today, buyers can rest assured because most manufacturers of these plugs have improvised their engineering. The plugs are safer than before.