Do the Clothes Make the Chaplain?

This week, my rant is about the assumptions many hospital staff and patients put onto a chaplain based on what we wear or don't wear. It's annoying because they just assume that you are whatever faith or religion they are without asking. Again, it's a form of passing.
First, every hospital has different guidelines for what chaplains wear. Some have specific-color scrubs for chaplains and just a badge, so you look much like other clinical staff (I think I'd prefer this.) Other hospitals use fancy lab coats with "chaplain" embroidered on a pocket, but I find this too authoritative and off-putting. Hospitals like the one where I work are ok with standard professional dress casual with maybe a tie. Our chaplains can wear a clerical collar, like Catholics or Episcopalians, if they wish. Generally, no other religious symbols are allowed, however, like jewelry, unless it is required by your faith tradition. For example, a Jewish male chaplain can wear his kippah and a female Muslim chaplain her hijab. The goal behind all of this is so that folks who are of different spiritual traditions don't instantly feel excluded. The intention is that we are everyone's chaplain, even those who may be atheists or "spiritual but not religious."
As a Pagan like me, dress isn't a big thing, which makes it easy. My ordaining body, Sacred Well Congregation, doesn't have any clothing requirements for professional work. And I like it that way. But the problem is that everyone in the hospital instantly assumes I'm Christian. This is also a challenge if I happen to meet a patient who is Pagan but doesn't reveal it. How would they know I'm a kindred spirit? Sure, I could likely wear a ring with a pentacle on it, and maybe they'd see it (or not). Chances are an eagle-eyed Christian patient would spot it and freak out, and that isn't something I want.
I've heard colleagues and friends offer a different perspective, that they'd like chaplains to be more identifiable, more like a traditional Catholic priest. They want to instantly know who they're dealing with, and I see the benefits here. Some patients, for example, think I'm a doctor when I walk in because I am wearing a tie. Some staff have to scan my badge first before they ID me. Honestly, wearing business casual does send the vibe of "middle management administrative dude" rather than chaplain for spiritual care provider.
On the other hand, one of our other chaplains arrived for a shift the other week really dressed up. He attends a nondenominational, Pentecostal-flavored church but showed up wearing a nice gray suit, clerical collar and big ol' cross necklace. Overall, he looked great. It did say, "I'm a chaplain" without a doubt. But as I thought more about it, it also felt intimidating. If I were a Jewish, Muslim, Pagan, Buddhist or other non-Christian chaplain, I likely would've felt, "Great, here comes the preacher to convert me in the Emergency Room. That's all I need."
So what to do? Part of me wishes I could find a way to signal to other religions or folks who have none that I'm there to support them, that I'm a "safe space," so to speak. You know, like the proverbial TV alien who arrives and says, "We come in peace."