This is not true. You can wear other colors and not be in violation of tznius. Of course, some groups are against bright red, but other colors are free game. Those groups likely do follow the idea that tznius means avoiding standing out, so day-glo colors and neon colors would be frowned upon, as would any other way of dressing that "stands out."
This limitation on colors is what's called a chumrah, not halacha. Of course, there will always be people who say that X chumrah is "straight up halacha." The halacha of tznius is quite minimal, but the chumrahs and customs have become pretty extensive. Most orthodox groups allow you to express your personality through your clothing so long as you are appropriately covered.
That said, black, white, and blue are predominant colors in tznius communities simply because a) they're flattering and b) tznius clothes are generally made for an "older" consumer (rather than the Jewish community), and elderly consumers tend to dress conservatively. Even I, the queen of color, own a ridiculous amount of black clothing because it's very flattering. And that's what's available in the stores.
But yes, there are orthodox groups that have very strict standards on both what clothing and what colors can be worn in order to be accepted by that community. However, 95% or more of American conversion candidates will not end up in these groups. To begin with, these groups are very hard to break into. They are generally suspicious of outsiders. Rightfully so, they're even more suspicious than average orthodox Jews that people would willingly take on the community's regulations without being born into it. Secondly, most Americans balk at that kind of groupthink/peer pressure, especially people willing to leave prior group associations and create a new identity. Most conversion candidates are strong free-thinkers or they wouldn't have ended up here. We also tend to have non-conformist backgrounds: hippies, political activists, pagans, individualists, etc. On the other hand, converts with pre-existing romantic partners are probably already labeled "too Jewish" for being orthodox, so even those predisposed to those kind of "cohesive" groups may not feel it is an option. Also, I would guess the majority of converts don't live in a city that has that kind of community. So unless and until you move, any decision to dress like a "right-wing" group is a personal choice rather than actually joining a "right-wing" community.
So keep on being who you are, which we inevitably reflect through our dress. If you are in the community right for you, this will not be a problem. If you are following the covering requirements for tznius (and that does not include wrist-length sleeves, ankle-length skirts, or mandatory socks/stockings), but are suffering social pressure about it, you should consider whether you are in the wrong community for you. There is a place within orthodoxy for everyone.