Terminal command for removing all named files except for one
The following will delete all files named File (and only those) within the current folder, except ones with extension .out:

find . -type f \( -iname "File.*" ! -iname "*.out" \) -delete -maxdepth 1

If you want to perform this operation recursively (traversing all subfolders), remove -maxdepth 1:

find . -type f \( -iname "File.*" ! -iname "*.out" \) -delete

The i in -iname performs a case-insensitive search, so file.*, FILE.*, etc. will be deleted as well. Likewise, file.OUT would be spared.