I am also having this issue using the Better MC modpack v9 using thonkutil-2.15.4+1.19.jar

You can add a datapack to make them wearable with Trinkets.
Path: /world/datapacks/=your mod or server name=/data/trinkets/tags/items/chest/cape.json
{ "replace": false, "values": [ "thonkutil:bacon_cape", "thonkutil:animated_christmas_2010_cape", "thonkutil:better_optifine_cape", "thonkutil:birthday_cape", "thonkutil:chinese_translator_cape", "thonkutil:christmas_2010_cape", "thonkutil:cobalt_cape", "thonkutil:dannybstyle_cape", "thonkutil:first_birthday_cape", "thonkutil:founders_cape", "thonkutil:hero_cape", "thonkutil:japanese_translator_cape", "thonkutil:julian_clark_cape", "thonkutil:mapmaker_cape", "thonkutil:migration_cape", "thonkutil:minecon_2011_cape", "thonkutil:minecon_2012_cape", "thonkutil:minecon_2013_cape", "thonkutil:minecon_2015_cape", "thonkutil:minecon_2016_cape", "thonkutil:mojang_cape", "thonkutil:mojang_classic_cape", "thonkutil:mojang_studios_cape", "thonkutil:mojira_moderator_cape", "thonkutil:mrmessiah_cape", "thonkutil:new_year_2011_cape", "thonkutil:one_millionth_cape", "thonkutil:optifine_cape", "thonkutil:pan_cape", "thonkutil:prismarine_cape", "thonkutil:scrolls_champion_cape", "thonkutil:translator_cape", "thonkutil:turtle_cape" ] }

So this either doesn't work, or I am doing something wrong, as I've tried it, but nothing changed, I rebooted server after making the file there.

Same issue is happening to me. I'd also want it to work without datapacks, as I'd need it to work on every world.