Here is some info for how Shame Resistance works (based on version 1.04, in case that makes a difference).
The following skills/titles (which appear in the Memories menu) affect Shame Resistance:
Note that the above skills might not immediately unlock after satisfying the requirements. Talking to an NPC can force the game to check if the requirements are satisfied for any of them.
Additionally, the 'Special' piece of equipment
Sealing Eyepatch raises Shame Resistance by 15, but it seems to be bugged -- when I used it to reach a threshold for more outfits, I still couldn't wear those outfits. The teacher in the photo club can synthesize this item.
You can get the webcam by talking to the guy at the top of the photo clubroom after unlocking Screwtube on your computer. You can unlock Screwtube by attempting certain Free missions, such as the Renegade Suppression mission which becomes available in Chapter 2. It doesn't matter whether you succeed or fail the mission.
Ways to increase Shame Experience (to unlock the relevant skills/titles) include: letting the guy by the School's stairs look up your skirt, selling your tights Downtown, using your webcam to stream "something sexy".
Ways to increase Exposure Experience (to unlock the relevant skills/titles) include: letting the guy in the Outdoor Mall look up your skirt, using your webcam to stream "something sexy".
Increasing Shame Resistance lets you wear the lewder outfits (which should be obvious from their descriptions). It's also required for some scenes, e.g. you need at least 50 shame resist to have sex in the men's bath at Oasis. Once your Shame Resistance reaches 50 you can leave the house while cum-stained. Once your Shame Resistance reaches 100 you can wander around without clothes on.