The Hashiras would likely show concern. Some, like Shinobu, would immediately start looking into possible medical solutions. Giyuu might be more reserved in his worry but would still keep a close eye on Tanjiro. The other demon slayers would also be affected. They look up to Tanjiro, so his sickness would lower the morale of the group. They would try to support each other while waiting for Tanjiro to recover.
Well, some characters might be amused. For example, Atsushi could be a bit shocked at first, seeing the different interpretations of Dazai in the fanfiction. He might find some of the more out - there scenarios quite strange but also interesting in a way.
Tanjiro might use his sense of smell to detect hidden threats. Since his sense of smell is super - enhanced, he could sniff out any demons or traps in the way of saving Rengoku. For example, if there are demons disguised as allies, Tanjiro would be able to tell by their scent.