Why You Shouldn't Remove Metadata from Your Photos
Removing metadata might seem like a good idea, but you may need it in the future.
Reasons to Remove Exif & XMP Metadata
If you don't want people to see camera settings, GPS coordinates (if your camera supports them) or you simply don't want other people to see how you edit your photos, you'll want to remove Exif and XMP from your photos.
These are all valid reasons, but you should always keep the versions with metadata somewhere. Here's why:
Why You Should Not Do It
The reason is simple: you may need that information in the future.
Metadata contains many useful settings (Lightroom edits, camera and lens model, camera settings).
After some time you might revisit your photos and wonder how you took that shot, what edits you made, what lens you used, what aperture, what was the time of day the photo was taken. If you remove metadata, you'll get rid of all this information.
If you spent a lot of time refining your edits or creating your own presets, you should always have a back up somewhere.
When your hard drive dies or Lightroom loses your presets, it'll still be possible to recover them from your exported JPGs – but if you strip Exif and XMP metadata on export, you won't be able to recover anything.
What Should I do then?
You should always keep the original exports with metadata included. Store them somewhere safe, back them up in the cloud (Dropbox or similar), so you'll have access to them in the future.
If you don't want other people to see your settings, before you upload files anywhere, create copies and run them through some kind of software that will remove metadata without re-compressing the image (e.g. ImageOptim).