With the Plex LG app, the only way to avoid burning in subtitles is to use text subtitles and audio that does not transcode.
If the video is transcoding and subtitles are enabled, they will be burned into the video stream.
You do have some options.
If the movie does not have a supported audio track (AC3/EAC3/AAC), you can add one using tools such as XMedia Recode. You can use it to transcode dts/TrueHD/etc audio tracks to formats that do not transcode, such as AC3/EAC3/AAC. Set XMedia Recode to copy the video track and convert the audio track (you can keep the original audio track if desired). Converting audio is not CPU intensive and takes a few minutes.
Another alternative is to use a different Plex client such as a Amazon FireTV 4K or Nvidia Shield Pro. Plex Android TV clients direct play subtitles, including when the video or audio is transcoding (Release Notes).
I do not know how other Plex clients such as the AppleTV and Roku handle subtitles.
