I think it’s a combination of things?
Overall, people are going to ship the Yu boys and the bracelet girls, regardless if they’ve had screentime together or not. That’s a given.
More specifically, we have Yugo’s dedication to finding Rin, which is very telling. We see this same devotion in Yuya and Yuto towards Yuzu and Ruri (respectively), but what makes the two of them different is that they also have the overarching goal of defeating Academia. Yugo blamed Yuto for Rin’s disappearance, implying that he doesn’t know that it was really Academia who was behind it. This means that Yugo has no reason to target Academia (as far as we know), making finding Rin his only goal. Unlike everyone else, he doesn’t seem to have any allies of his own, and he’s willing to fight both Academia and the Resistance in order to find Rin. This is an incredible show of devotion, and can very easily be interpreted as romantic (at least, on Yugo’s end).
As for the feeling being mutual? It’s hard to speak for Rin, seeing as she has yet to make an appearance, but we may be able to infer some of her feelings towards Yugo. When Yugo first saw Yuzu and mistook her for Rin, he didn’t hesitate to hug her. Something like that may seem pretty innocent to us, but it’s pretty telling when you look at it in the context of the show. For example, Yuya and Yuzu are close, and yet very rarely have physical contact–the only time they’ve ever hugged was in episode 9, and it was quickly broken up when Masumi “Mood Killer” Kotsu brought up its romantic context. Comparing that to the way Yugo treated “Rin”, and it really makes you wonder.
Of course, that hug may have been there to show how Yugo’s missed Rin so much that he’s willing to throw all proprieties out the window. Or maybe it was meant to speak to Yugo’s lack of intelligence. Either way, I don’t think that Yugo would do anything that Rin wasn’t okay with––by the way Yuri described her, she’s probably just as strong willed as the other bracelet girls. So if his first reaction to “finding” her was to hug her, then physical contact with Yugo may be something that Rin is totally okay with. It’s something to consider.
Mind you, I don’t ship them (yet). I currently consider them to be plutonic soulmates, and only when Rin actually makes an appearance will that be subject to change.