Well, ignoring the meaningless guilt by association tactics ("fox-news-worthy neocon propaganda"), it's quite simple.
I don't care about being "forward-thinking". I care deeply about freedom. I have relatively idiosyncratic views, but I align myself largely with the libertarians except on a few social issues.
I just don't think people should be forced to do things except in very specific and limited circumstances.
I find the examples you bring up rather interesting. First, I think the right/left political system in America implied by your choice of topics is a false dichotomy. I don't think the two sides are really all that different at the core.
Pepsi in schools is a non-issue to me. My problem there is the schools themselves - this is a different argument, and I'll have it in a different comment if you want to have it. So no, I don't think it should be banned.
The immigration question is very difficult, and brings up many issues such as the real role of nations and the importance of citizenship. I haven't completely made up my mind on the issue, but I think both the major positions are wrong.
Really, I think immigration wouldn't be an issue if it weren't for the cancerous explosion of government in the first place. One of the biggest problems the Right has with immigrants (other than racism, which exists and which I eschew), is that they gain access to socialized benefits they didn't have to support. I don't think the government should be forcing people to pay for these social benefits in the first place, with a few very limited exceptions.
That said, there are many other facets to the issue, so I'm not going to take any definite stand on the issue as a whole at this point.