If you go for a reputable provider, the servers should be as safe as any out there. That said, even the best free Minecraft server hosting usually offers limited resources, lacks many features, and has too many players per machine. This can lead to poor game performance and usually prevents you from running any game mods.
Essentially, free providers bet the free plan will not be enough for you, and you will pay to upgrade. And, when you upgrade, the hosting will likely be more expensive since the provider needs to cover the costs of supporting all the free users. A paid provider usually performs better and has more affordable scaling.