Is it safe to allow apps to access storage?

These are the permission types to pay attention to when downloading a new app:

If you allow the storage permission it can access the data ,in case of data breach or any other leaks app can allow its self to get the data. If app is encrypted for prevention of data breach your data is safe rather than may be your personal data is not secure.17 May 2019

Yes. The storage permission grants an app access to the whole “Internal SD Card”, where all your photos, musics, downloads reside . It’s usually safe to assume that apps you trust access only what they need, but a random unknown app may scan your files and expose some privacy problem.24 Eyl 2018

Storage permission is needed by apps that will read/write files onto the storage especially files accessible by the user .