The definition of a "cult" is a small group of people who hold the same beliefs. All religions started as "cults". Christianity began as a persecuted cult in the Roman Empire. It now has over a billion and a half followers. So yes, a cult can definitely become very "mainstream".
The term "cult" is a relative word. It depends on where you are and what you believe. If you have beliefs that are very close to the Jehovah's Witnesses, for example, you would not consider them to be a cult. You would probably consider them to be a religion. If your beliefs are quite far from theirs, you could easily label them as a cult.
Yes, I believe a cult can become a somewhat acceptable religion, if it has enough members, financial backing, and media attention. Many people liken the Church of Scientology to a cult and it has become remarkably popular as an accepted religion, although it seems to cater to the more affluent.
I do not believe a cult can become an acceptable real religion. That doesn't mean it doesn't happen under the laws of the United States government or other governments. Religion is a tricky subject because, as a country, we want to provide religious freedom, but that also requires a very open mind to accept different religions. Cults probably don't make the cut, but if they have followers and meet the classifications of religion, then they deserve protection. So, it really depends on how a person decides rather something is acceptable or not.
I do not think that a cult can ever be an accept religion. I think that some cults are just too far out there that some people will not ever accept them for being anything more than a place where some people just follow a strange belief. I think that people should respect people's rights though.