Fabulously Optimized supports various OptiFine features, including resource pack extras. However, the implementation differs from mod to mod and some resource packs are accepted in OptiFine even if they are broken, so this page should help you fix some of those issues.
Is the resource pack actually built for the version you're running? If not, check for the latest version or use a converter tool like this one or the official one.
If you see this message while activating a resource pack:
Contains broken paths
This means the resource pack maker is using spaces or other non-standard characters in the file or folder names.
If this is the case, the modpack will warn you and allow overriding it, but note that various glitches may occur (miscolored or invisible blocks, lightning issues, broken textures...).
To fix that, please tell the resource pack maker to only use the following characters in file/folder names: a-z0-9._-.
Fabulously Optimized does not plan to add "fullbright" methods beyond its current dynamic lighting, because it would take away from vanilla gameplay's night vision and may be disallowed on certain servers' rules.
This may occur when the pack is using broken paths and is trying to change the models of some blocks, like chests.
Enhanced Block Entities
Enhanced Block Entities is the mod that makes various blocks faster on most versions of FO. Some optimizations may not be supported by your resource packs, so here's how to configure it:
Search for "Enhanced Block Entities", click the config button
Enable "Force Resource Pack Compatibility"
If that doesn't help or the option is not visible, disable any blocks that seem broken to you. Usually disabling Enhanced Chests is enough.
Some versions of FO include Better Beds instead.
Close the game
Remove or disable the Better Beds mod from your launcher.
Start the game and see if it is fixed.
FastChest (FO 1.12.3 and older)
Search for "FastChest", click the config button
Disable the mod, click Done.
Does the resource pack change the UI beyond usual means (e.g. rearrange HUD elements)?
That means it may depend on core shaders, which are not fully supported on FO.
Coloring blocks differently by biome is currently not supported since FO 4.5.7, but planned to be reintroduced soon.