Here's a theory: Ishid, in the original storyline, was also interested in Yunifer at first. As he watched her from afar, he also ended up watching Raele as both of them were friends back then. So in this original plotline, there is no bad blood and he knows her as his crush's friend. Then later, when he realizes how much she's suffering because of the crown prince, he sympathizes with Raele and ends up falling for her, unknowingly breaking Yunifer's heart who liked him to.
In this storyline though, Yunifer didn't want to be Raele's friend anymore and kept trying to avoid her. Raele, though, followed Yunifer everywhere and thus Ishid came to see her as an eyesore who was aiming for Yunifer's attention when he himself couldn't get it or bring himself to ask for it. This whole backstory then explains why they give off a feeling of competitiveness.