It depends how it's written, to be honest. I've had 'frenemies' in the past. People who I was long time friends with that I either had a personal/professional rivalry with or just didn't agree with much of their world view. It's not enough to make me not want to be friends with them, but it's enough to have a little tension since we disagree on many subjects.
To me, Merrill, Sebastian, Anders, and Fenris are the most ridiculous ones. To rival them, you really need to challenge some core beliefs of theirs; beliefs that they are very passionate about.
But for Aveline, Isabela, and Varric, it's more about having a different outlook on life. And that's easier to understand than the other examples. We've all had those friends where we're like, "Ugh, really? Again with this?" and usually it's not enough to make us want to ditch them as friends altogether.
I love frienemies in fiction, and I feel like I've had frienemies in real life, usually coworkers. One guy I work with and I have bickered a lot, and sometimes we argue over nothing, but we also joke. We also talk freely in a group get togethers outside of work and rib each other. Every once and a while, he says something boorish and I tell him that he's a jackass. He usually says that he knows he is. I find him unlikable, arrogant, and occasionally bigoted, but I can hang around with him and I would try to save him from drowning if it came to that.
I even have a few frienemy types on the forums, come to think of it.
Anyway, I didn't think it was so ridiculous that Merrill and Fenris would stick around with the rivalry path. After all, Merrill did tell a rivaled Hawke to get out with uncharacteristic fury. I've always thought that an important factor there is that in keeping the shard Hawke might be breaking her heart and crushing her dreams, but they are doing do at the behest of Marethari, the other person Merrill can love enough to forgive hurting her so deeply and it's easy for her to believe that Hawke is doing so for the same reasons, to try to protect her. I always imagined that it took months for unromanced Merrill to sort of forgive Hawke again after that, but I don't think it's so ridiculous that she could. Eventually.
As for Fenris, he's so alone. He doesn't really feel like he sees eye to eye with anyone. I feel like if he were to have a friendship meter with each other companion, most of them would default to the rivalry side, the only exceptions being Sebastian and Aveline. What's one more person to be at odds with? At least he thinks he can trust Hawke, and he can growl at him about their disagreements as an equal. I think he finds that preferable to being alone.