Well, it doesn't have to.
I wrote a while back about the special challenges that face conversion candidates who want to live as Lubavitch chossids. But even in those worst-case-scenario circumstances where you may have to leave your Chabad shul and rabbi until the conversion is over, nothing prevents you from going back once the conversion is over. And most people who leaned that way early in the process do go back after, though I can't say how many stay long-term. I think they needed to go back to see if it really was the place for them, and sometimes it's not. It's tying up loose ends, in a sense. Especially when a short-sighted blanket prohibition on Chabad was part of the conversion. That tactic works just as well with conversion candidates as it does with teenagers.
Why does this work? The RCA does not espouse any particular hashkafa. Remember that the RCA is essentially just a licensing agency that allows independent batei din to use their name and support. Your particular beit din may have a specific hashkafa, such as many of the yeshivish and chassidishe batei din, most (all?) of which are not RCA batei dins. In those cases, you may be expected to toe the line to that particular hashkafah, but that should be a consideration before you sign on with that particular group.
As you go through the RCA process, you can choose to affiliate Polish Ashkenazi, Hungarian Ashkenazi, Yekke, Yeminite, Iraqi Sephardi, Dutch, whatever. Most people don't convert that specifically, sticking to general Ashkenazi or Sephardi designations.
What determines your customs? Among other things, the community you convert in, the rabbi(s) you work with, and your personal ethnic history, especially if you have some Jewish ancestry from a particular area. But even if you go general, you will still be a mix and mish-mash of many minhagim because American and Israeli communities (and many communities worldwide) are usually a mish-mash of people from everywhere. And so many intermarriages between different types of Jews have created many families with mixed minhagim. So, at best, you are probably "Ashkenazi by default" if you convert in the United States. You could easily end up "Sephardi by default" in Israel or some other communities. Nothing wrong with it, except from the people who refuse to see the reality that a "community standard" doesn't exist in most places today.
Rather than just focusing on the Lubavitch candidate, let's try some other scenarios. Let's say you convert in Atlanta with the RCA-approved beit din there and you convert through a middle-of-the-road orthodox shul. That doesn't mean that as you learn and grow and move through life that you can't move to the right and become yeshivish or move left. Likewise, if you convert yeshivish, you're not prevented from becoming chassidic later on. Marriage often influences these major shifts, as opposed to the subtler shifts we all have.
Where you are haskhafically when you convert is just one moment in time. Every Jew is (should be) growing, changing, learning all the time, for the rest of your life. We all go through periods of more or less stringent observance. Different things speak to us in different seasons of life or life circumstances. And there will probably be a period or two (or more) of anger and rebellion. Congrats, that means you're really Jewish.
Don't be afraid that your conversion seals in what kind of Jew you'll be for the rest of your life. It doesn't, and it can't.