Mechanics aside (which gentlemen Gerrark and magikot described before me in great detail), I like this card because of its flavor. And this review will describe flavor only - if you are looking for actual applications of this piece, feel free to scroll past.
What is the Starlight Crusade? The art on the card I have recalled describes a woman that looks slightly like a nun, with a crucifix on her neck and a white clerical collar. Are they neo-christians? Well, no, even though they like to point at their link to medieval age Order of Templars. What is more accurate is comparing the Crusade to church described in P. K. Dick's 'Do androids dream of electric sheep?' - the Cult of Mercer.
Said worship included interfacing with a machine that, connected to a brain, would allow you to join minds with other believers and the cult's messiah Mercer himself as he walked uphill surrounded by people hurling rocks at him, letting you live through his cathartic suffering again and again in order to cultivate empathy. So-called 'Meditation Booths' technically have a similar idea behind them - neuroscience is the big thing in the world of Android, allowing the researchers to pinpoint the areas of the brain that govern mystical sensations. Starlight Booths stimulate these areas, giving you sense of enlightment, but devoid of any content and regardless of your personal views or imaginations about the afterlife. So while it fulfills social functions of a religion (which would be comforting you and giving you sense of stability), even despite it having some philosophy behind it (which, quite frankly, looks like some patchwork made from hindu and buddhist teachings more than something legitimate), it absolutely fails to do what religions were meant to do in the first place - give answers. A perfect cult for a consumerist world, putting instant gratification over delving deep.
Being a follower of Starlight Crusade would involve attending these booths in order to reach further 'levels of enlightment', which would mean readying your brain for even higher levels of stimulation. Of course, the organization charges you for using their contraptions, the higher the more enlightened you are.
So, the first effect of the card, the tag removal, is more of blending in with the crowd inside the Starlight Citadel than anything. The corps are looking for you, but since you're hiding away amongst some shady techno-sect, recently famous and well-regarded for giving refuge to those harmed during the Flashpoint crisis, they have to be extra careful trying to get to you. The second effect is more interesting.
How does a religious practice prevent getting a rocket to the face? Are you suddenly able to stop the missiles with the power of your will? Can you dodge a bullet because you are the One? No. We are to assume that you are physically hiding inside a booth when the Corp tries to come and get you. These things are built to last, but only so much when met with heavy firepower. The side effect is that the machine activates when you are inside, serving you - willing or not - mystical visions when the soothing impulses are delivered into your cerebral cortex. Whatever was important at the moment - the cards in your grip - becomes washed away with sensation of omniscience and you walk out completely bare-minded.
EDIT 9/11/2019, super reminiscing revisition edition! Yep. Completely missed the parallel to the Church of Scientology there. My bad.