I've been thinking about this a bit and finally am coming to some kind of conclusion. I'll be talking about romantic relationships.
To start with, if a person informs somebody (e.g. a new partner) that they will not compromise on things, ever, it is very likely that they are the most selfish jerk kind there is.
However, I think culturally there is way too much emphasis on compromising. Everybody's heard the relationship-truths that say "compromises are necessary in a relationship" a thousand times. And I don't wholly disagree, as I do think it is likely that there will occasionally be something. But there are two reasons why it is way more rare than is implied by the common understandings.
Firstly, compromises are only needed in decisions which concern both (or all) people involved. Culturally supported view of a relationship is, in my opinion, somewhat co-dependent. At least, I don't think there is enough emphasis on personal boundaries; certainly less than there is on the necessity of compromising. This is why in a couple relationship it is often the case that pretty much everything either one does is viewed as a decision that concern both persons, when actually there is no reason they would be common decisions.
Secondly, if partners are on the same side, there is quite little need for compromising. Compromise, as I understand it, refers to two (or more but two is simplest) people on the opposite sides, both of whom are primarily interested in getting their own way as far as they can; then they come together and, due to not being selfish jerks and having heard that in a relationship compromises are necessary, they calculate the middle point and do that. That is certainly better than one person dominating, and the other sacrificing. But that is the problem: this culturally supported view that either there are compromises or there is dominance.
What I want is not that my partner takes my feelings and wants into consideration and then compromises with me. Even less, of course, I want a partner who doesn't care how I feel or what I want. But, what I want is a partner who thinks my getting what I want is as important as them getting what they want. I am obviously prepared to have the same attitude towards them. Now, this doesn't negate the fact that the both of us are still responsible for our own wants. With proper boundaries both can exist simultaneously.
I don't have time to get into it more right now, and it is quite abstract, but if that doesn't seem understandable, please ask for clarification. Otherwise, I'd like to hear other's views.