Is it is rude or unprofessional to ask for this? If not, how should one approach the company?
It is not rude.
Regarding professionalism, this depends a lot on the position, your responsibilities and the project you are working on. In some cases it may be OK (or even expected), in some it may be unprofessional.
I want a MAC or Linux environment. I don't want a windows environment.
Is this a Windows project? If so, then asking for a Mac or Linux will be unprofessional, because developing on a Mac (or Linux) for windows platform, is a bad professional choice (it introduces difficulties in the process that should simply not be there). Asking for a Mac/Linux for compiling a WinAPI project for example, will show you have no idea of the project in general ( compiling WinAPI on a Mac will be ... difficult :) ).
On the other hand, if it's a cross-platform project and half the team uses Linux, then you can probably ask for one as well, without appearing unprofessional.
If you use any specialized tools (IDE, source control, etc), making them run on the new platform may be costly or impossible (e.g. if everybody uses projects for Visual Studio and you edit using vim on Linux), you can edit project files manually (and possibly screw them up) or you can duplicate a lot of the team's effort, by maintaining you own development environment sparately.
Then, you get to security and availability: development environment may require special access (different accounts and domains for example), resources that are optimized for windows-only access, Windows-only tools (like TFS) and so on.
There are also some problems with cost and licensing:
getting a mac costs a lot (more than getting a PC):
if the company doesn't already have them in stock, somebody will probably not like having to dish out money for a mac, just for you.
there may be licenses involved in switching, and even if there are not, lots of corporate environments have a legal department responsible for licensing issues, so even if the licensing of the tools involved impose no conflicts, (like "do not use this tool for commercial projects") it is possible you will get approval for this, only after this department confirms this officially.
Asking for such a switch also asks for administrator time for installations, configuration, and ongoing maintenance.
Basically, expect a lot of hidden costs.
A professional way to ask for such a change, would include a well argued list of bennefits comming from the switch (provided to your manager) and an acknowledgement of the costs involved and why they are worth it.
Your personal preference should not enter into it, unless you addressed this in the interview (as in "please keep in mind that my main expertise is Mac development and I have no Windows experience at all" - and they accepted this when you were hired).