PS> I have updated several Odlrim/LE converted "UNP" (ish) followers using the BHUNP body.
As long as you output the results of your bodyslide work to a custom folder, then transfer only the resultant meshes (and tri files if you're ensuring racemenu realtime adjustment support) to the character's mesh folder, you should be ok.
For working on the player, make sure that you use only the correct type of preset with the body build efforts. That is, while you may like some random bodyslide preset, unless it is made to be used with the body type you have installed, you're going to get some weird results like that shown in both your example image and in mine.
My advise is simple... For the player, if you have CBBE installed, use only CBBE presets. If you have CBBE Advanced installed, use only CBBE Advanced presets (Bodyslide uses Body/outfit and Preset to configure the fit), if you have 3BBB installed (and while you could use CBBE preset) use only 3BBB presets to ensure it acts as it is supposed to work.
If you're working on a UNP follower, you can "upgrade to BHUNP" by using a BHUNP preset that matches or closely resembles the original UNP follower, but it will likely require tuning the preset (then saving it as "this_special_followers_name" so you can access your work later on), but to avoid weird seam issues or other muck, only the mesh output should be transferred to the custom follower's mesh folder (requires changing the output path to some dummy working folder or it will overwrite your player body), and any texture changes(adding tats, or "special" body textures" should also be manually completed using blender or Paint dot Net or similar to edit a copy of the original textures, and then used to replace the original texture files (ie edit the original texture files and modify those) again by manual insertion.
Hopefully I don't have to say it, but for clarity's sake, also make sure when building your player body (and hands and feet to avoid seam issues), if you decided to install 3BBB, use a 3BBB Body spec for the Body/Outfit selection, if CBBE, use a CBBE Body/Outfit, etc. Sma ebasic advise for any follower/NPC you fiddle with, except that they should NOT use CBBE assets UNLESS they are natively CBBE
And imo anyway, ALWAYS check the "Build Morphs" checkbox to ensure that later you can perform realtime adjustment in-game using racemenu.
edited for content