Peaceful but distant relationship. I can imagine superficial admiration from Merida's side but that's all. Mulan would be quite cold to Merida and prefer more dutiful and family-oriented princesses. I think Merida would be only DP Mulan would have negative feelings towards, despite Jasmine being Mulan's true opposite.

Not a fan of bromance between them, not at all.

^ I agree, but I also feel that they would be able to bond over training with their bows and weapons and Mulan could teach Merida how to value her family more while helping her learn more skills, such as sword fighting.

^ Not a fan of idea that Mulan is so passionate about weapons that can become friends with anyone who loves them. Really, really not a fan. Neither I like couple dynamics which includes one half of couple changing core values of other. I prefer couples between people whose core(!) values are same. But to each his own.

Both have different personalities but similar interest. I think Merida can help bring Mulan's more extroverted side.