Yes, this can be normal. Lightroom may show different versions of the same photo in Library and Develop.

A common reason is that the Library module can display the JPEG preview embedded in the raw file, which was generated in-camera using the camera’s own color settings. The Develop module, however, renders the raw data itself using Lightroom’s default profile and processing, so the color can shift warmer, cooler, or more red.

So the difference is often not that Lightroom is “adding red,” but that you’re seeing two different renderings of the image.

If the issue is with exported files looking wrong in another program, make sure the exported image includes an embedded color profile so other software can display it correctly.

In short: yes, this behavior is normal in many raw workflows, and it is usually related to preview/rendering and color profile handling rather than a problem with your photo.