You are not very specific: on the one hand, there is more than one kind of mathematical writing; on the other hand, you write "I am concerned this may tarnish my reputation" and that depends (a little bit, at least) on who you are.
I will assume that you are a junior mathematical writer, i.e., that you have not yet published many (or any) mathematical papers. (If you have already written a few dozen papers, you have not only a lot of experience but have gotten a lot of feedback, so you know what kinds of writing variations referees, editors and other careful readers will pay attention to.)
Let me begin with some (unfortunately rather conservative, but still inherently sound) advice for the journeyman writer in any academic field:
Don't try to be innovative or different in your writing style in your first papers or first years of writing papers. First learn how to write acceptably -- or better, well -- according to the most standard norms of your discipline.
It takes a while to master the standard conventions of academic writing. When I look back at some of my earliest papers, I see some weird stuff. In a few cases I was trying to be innovative, but most of the time I just didn't know what the standard convention was. About 50 papers in, I am still learning new things about the standard mathematical style.
What's so great about standard mathematical style? Nothing inherent. But as a culture, we're used to it.
The cardinal goals of mathematical writing are precision and clarity. After that, the next goal is unobtrusiveness: good mathematical writing does not call attention to itself, because attention that is diverted to the writing is diverted away from the mathematical ideas and reasoning.
Again, what is unobtrusive depends on the culture. For instance, there are some mathematical turns of phrase that would be pretty weird in ordinary writing but are not weird in mathematical writing because they have been done so many times before. Examples include: "in the sequel," "by abuse of notation," "a trivial case"...And of course the best example is the use of "we" in mathematical writing. It looks pretty weird the first N times you see it...and then it doesn't. It is an entirely standard convention of mathematical writing, as can be seen by its approved use in virtually every mathematical style guide but even more strongly by its almost universal use in published papers. You don't have to use "we" in mathematical writing -- e.g. this style guide contains some tips from Paul Halmos on avoiding it -- but I can think of no good reason to avoid it.
Every mathematical style guide known to me denigrates the passive voice in mathematical writing in the majority of instances. So for a journeyman mathematical writer to insist on using the passive voice would be a violation of both of the above pieces of advice: on the one hand you are not learning to write in the standard way, and on the other hand you are writing in a nonstandard way that a lot of your readers are going to notice, get mildly distracted by, and therefore in some cases get moderately annoyed at you for writing in this way. Why do you want to risk this? You say:
"I am interested in using the passive voice in mathematical proofs as I feel that this reinforces the objectiveness and universality of the proof as opposed to the specific instance of the proof or my own self."
Honestly, I am very unsure what you mean by that. In case you are suggesting that there is some logical or ontological difference between
We will show first that A implies B and then that B does not imply A
It will be shown that A implies B and then that B does not imply A
I can assure you that there is not. More to the point, readers of math papers are not going to be critiquing the proofs for "objectiveness": I don't even know what it would mean for an otherwise satisfactory mathematical argument to lack objectiveness.
Moreover, what are you actually trying to accomplish by using the passive voice in your math papers? It can't be to make your work easier and more pleasant to read...as you seem to understand already. You write
"Would it be looked upon negatively to intentionally employ a writing style uncommon in my field to express what I see as key values in the field?"
What "key value" is expressed by using the passive voice? I don't think there is one. But if people get wind of the idea that you feel like you, as a junior person, are in personal possession of a clearer understanding of the "key values in the field"...Well, since you asked for feedback, my honest appraisal is that you sound a little nutty and a lot inexperienced. So it is a bit of a negative, yes. Of course, all mathematicians start out a lot inexperienced, and many, many of us are a little nutty, so your eccentric-sounding ideas about writing and mathematical values will not be a major sticking point in your career.
The largest issue I see, honestly, is the impediment to learning good writing that you've placed on yourself. Without meaning to be harsh: parts of your question remain obscure to me after repeated readings. The comments show that other readers feel the same way. This is a real example of your writing not being properly understood by others, perhaps to the point of your overall message getting lost. That's the risk you incur by not placing a premium on clarity. It's a big one.