How to bridge the compatability gap between different types of thinker? Do you have any general advice to productively discuss mathematics with others who have a different view? I mean for example algebraic thinkers and geometric thinkers. I don't want to isolate someone by forcing discussions to be framed in my own terms.
 A: I think that in conveying a willingness (and desire) to understand a given topic/question/problem from multiple points of view is key. For example, your statement "I don't want to isolate someone by forcing discussions to be framed in my own terms" goes a long way to such an end. 
Your question also suggests a sensitivity to others' ways of thinking, and it is clear you aim at being inclusive. Any thing you do in communicating, in advance, this sensitivity and desire for an inclusive dialogue/exchange will help diminish the prospect of inadvertently excluding those with different ideas/approaches from participating/engaging.
So being up-front with that willingness and desire for productive conversation by inviting different perspectives, is key. One might also want to preface one's contributions t0/perspectives on a given topic/question is helpful, to this end: e.g., "Looking at the problem from an algebraic perspective,...". 
This sort of approach and openness is crucial, too, if one has any hope to productively teach mathematics in a way that engages a diverse range of students, rather than trying to "force-feed" all students to accept one way of thinking and/or one way of approaching/solving a problem, and helps dissolve many students' resistance to learning mathematics.  Admitting in advance that you are discussing one way of thinking about a problem and/or solving it, and occasionally offering alternative approaches that also work encourages/invites students to think about mathematics and the problems they encounter in any number of ways, too.
EDIT: I don't know that I'm addressing the context in which your question emerges, or addressing the sorts of productive mathematical discussions about which you're concerned, but I think it's relevant to the question of how best to engage with others, mathematically, in any number of contexts.
