If you can ask the question: "Who is a Jew", many will ask: "Why" ?
Why do you ask that question ? If you can think of a good answer, fine, it is at least a starting point.
But, if your answer is, essentially, "because I say so", it's not going to fly anymore.
We have too many choices for religion, and too many ways to practice.
I believe Judaism must be very inclusive. We cannot exclude people for irrelevant reasons. We must adapt to a changing world....otherwise we are no different than Conservative Judaism, a shrinking denomination with little relevence.
Inclusivity is good. But recklessly inclusive of anything and everything, without question, is not good. Perhaps you've heard the expression, "Keep an open mind, but not so open that your brain falls out."
Every society, every culture, needs boundaries and rules to function, otherwise it quickly ceases to become an integrated, coherent phenomenon, and simply becomes a chaotic mess of individuals rapidly drifting away from one another into the random courses of their own whims. Thoughtless adaptation born of humanistic relativism and a blind desire to be acceptable to others is no adaptation or not, it's just sacrifice of one's own culture and identity to the chance currents of assimilation and cultural homogenization.
Yes, the Conservative movement is shrinking, largely because the age of movements is approaching its end. There was never really such a thing as an Orthodox movement to begin with-- Orthodoxy is simply a large bloc of communities of halachic Jews who share certain philosophies of halachah and observance to one degree or another. Eventually, there will simply be halachic Jews and non-halachic Jews, in independent and comparatively loosely related communities. Halachic Jews will consist of a relatively large number of charedi communities and a relatively small number of communities made up of people who would now identify either as Open Orthodox or center/right Conservative, with perhaps a small sprinkling of Reconstructionists. Non-halachic Jews will consist of a small number of communities with precariously balanced standards hearkening back in some way to tradition, made up of people who would now identify as left-wing Conservative, right-wing Reform Jews, with some Reconstructionists; and a large number of communities of people who are not halachically Jewish, know virtually nothing about Judaism and Jewish text and tradition, but self-identify in some fashion as Jews, made up of people who would now identify as center/left Reform, some Reconstructionist, and various fringe elements from Renewal, from secular or humanistic Judaism, from Messianic Judaism, and so forth.
The shrinkage of the Conservative movement, in other words, has nothing to do with the relevance of what Conservative scholarship teaches; it is simply an attendant phenomenon of the next alteration in how the global Jewish community will arrange and identify itself.
Having an answer to the question "Who is a Jew" is not about power, mostly because the people who feel oppressed by having an answer to that question are not Jews themselves, or they are so very far to the radical leftmost fringe of Judaism that they were never in a position of any authority or recognition anywhere in the main stream of Jewish thought anyhow.
Having an answer to that question is simply about being able to easily and readily determine: when we make a minyan, when we need halachic witnesses, when we are considering marriages and divorces, when we are deciding whose kids shall be given space in our congregations for bar/bat mitzvah celebrations, when we need Torah readers or wish to call people for aliyot, when we need a mizumin for birkat hamazon, and so on-- who may qualify, and who may not? And secondarily, when we have discussions within the Jewish community about issues relevant to our beliefs, our traditions, our halachah, our issues of identity and self-direction-- who should have a voice, and who should not?
If a person is committed to living a Jewish life, participating in Jewish ritual, and being a part of the conversations of the Jewish People, it should be entirely appropriate and reasonable for them to convert properly, presuming that they were not born to Jewish mothers. If this is a problem for them, the question must be asked: why, if their commitment to being Jewish is so strong, is this relatively easy entry into being a Jew too much for them to do?