I think there's easier explanation for Mac's anxiety and dismay than notion that in some way using Placard breaks his neutrality (because it does not at least by letter by Accords) - simply I mean this is Relic of celestial nature, with power of Logos Incarnated behind it, ergo something Mac left long ago - and it's hard to say what's his current position on this choice.
I think it's sort of guilt, regret, and such things.
Yes, I think that may be more to the point than his neutrality or taking sides. I don't think Mac cares one way or the other if someone recognizes what he is, Vadderung seems to know, the Outsiders called him by name. Seeing the Placard and committing to what it stands for by smearing his blood on it, revisits a choice he made long ago, it will be interesting to see if this is a turning point and we see Mac evolving. Kind of like the shadow of Lasciel becoming Lash, yes, partly because of Harry, not unlike Mac, but a couple of more subtle personal things which I think were the real moments that began to change her. The first one was after Harry burned his hand so severely and Butters gave him a guitar to learn to play as physical therapy. Lasciel helped him and made a sad little comment with a hint of regret, she hadn't been able to make music in a very, very, long time. The second happened in Proven Guilty I believe, after he got back with Molly, Charity et all, they took refuge with Father Forthill. Harry wanders into the church proper and Lasciel now more Lash than Lasciel, says:
Lasciel's voide came to me, very quietly, and sounded odd. Sad. It is beautiful here.
Lasciel hadn't been reminded in a long long time what it was she gave up when she followed Lucifer, and she hadn't regretted her choice.. But I believe the two incidences began to make her maybe rethink a bit. I think when he put that blood on the Placard, Mac may not have regretted his choice all these years, but he may begin to rethink.