Look. It's like this. In D&D, your Religion, History, Arcana, and such skills like them are a measure of how much knowledge your character has on a particular topic. So, if you are proficient in Religion, that means you have some basic knowledge on the religions in Faerun.
Therefore, the entire point of having such skill proficiencies is so that when you, the player need to know something about a particular piece of lore in the world your character lives in, the DM calls for a dice roll. If you fail, you don't know about that thing and the DM describes nothing to you about it. If you succeed, you gain the knowledge from the DM. Usually, the higher you roll, the more the DM will tell you if you want to know more details.
So, if you fail your dice rolls in BG3 and therefore your character knows nothing about Shar and Selune, then that's the way things go. If your character is totally clueless by the time of Shadowheart's big reveal because you failed your Religion dice rolls when you first encountered items from Shar and/or Selune, then your character's dialogue choices during the big reveal should be more like, "Okay. Is this supposed to be a big deal? Who's Shar anyway?" as opposed to (if you made the Religion rolls successfully), "Whoa! You're a cleric of Shar? That's unacceptable. You MONSTER!" or "Hah! I knew it. You were throwing Shar flags all over the place," or "Hmmm. I kinda had a feeling, but I wasn't sure. Either way, it doesn't matter to me. You are one of us. I don't care who you serve." Or something similar.
Some ownership DOES have to be put on the player. If you're going to skip cutscenes that explain things, that's on you. That's like a player during TT having the DM explain something to them but they were zoning out and then wondering why they didn't know something later in the game. You zoned out. That's on you.
Whether you look up Shar information on the web or not, that shouldn't matter in regards to the game itself. Your character should only have dialogue options based on your character's knowledge of Shar. If you succeeded in the roll, you should know who Shar is and have appropriate responses based on your character knowing who Shar is. There should be options for outrage and dismissal because you simply won't accept a Sharran Cleric in your party and options for saying that you knew but didn't care. If you failed, and your character knows nothing about Shar, you should have options that are more based on trying to learn more about Shar and who she is and then trying to figure out what you are going to do about it.
But regardless, I would expect more responses from origin characters like Gale who loves Mystra who hates Shar. Gale shouldn't be flirting with Shadowheart when he first meets her but should be more distrusting her IF he knows she's a Sharran. I could see him hitting on her if he was clueless about her patron deity, but not flirting with her... unless he's totally lying about being a lover of Mystra. Wyll shouldn't like having a Sharran in the party, unless, of course, he's not really the hero wannabe he claims to be.
And overall, that armor shouldn't scream Shar. It should not look like the Justiciar armor found in Grymforge in any way. Shar's followers would NOT roam around Faerun in armor that screamed who they served. They are a secret society. The only time they'd wear armor like that is maybe if marching into some major battle, and then only if the need was there. Shadowheart is supposed to be on some covert mission. She would not be parading around in Shar armor.
