While the ActiveSync software that comes with the Axim is Windows-only, the Axim itself will work perfectly well with a Mac. You do NOT need ActiveSync to transfer files (movies, photos, music, etc.) between your Mac and Axim, nor do you need it to install software to your Axim. While ActiveSync can do these things, you can almost as easily (sometimes more easily) do them without ActiveSync.
The main thing ActiveSync does is synchronizing frequently changing data between programs on your Axim and your computer--and for as little as $14.95 you can buy Mac software that will do the same thing. For the most part, this means that, when you add or modify a calendar entry on your Axim, the same change is made in the calendar program on your computer, or vice versa. Ditto an address book entry. If you use your Axim to access an email account and you sometimes access that same account on your computer, then ActiveSync will also make sure those mail programs they show the same messages in your mailboxes (if you use a web-based email service like hotmail or gmail, you won't use this feature). If you don't care about keeping the same calendar, address book, and email on your Axim and computer, you don't need to sync at all. If you do want to sync, there are two companies making products you can use, Missing Sync and PocketMac (which has a $14.95 Lite version, which seems sufficient for most users). I don't have a Mac and can't recommend either program, although reviews on the web suggest the both work well for simple synching and file transfer.
Any of the sync programs will allow you to put your Axim in its cradle or on a sync/charge cable and then open up the Axim itself (or at least the memory cards in it) as a folder on your desktop. You can simply drag and drop files between it and your computer. However, for large files (movies, GPS maps, large dictionaries, big folders of music, etc.) this connection is annoyingly slow. You can transfer files without a sync program--and do it much faster--simply by taking a memory card out of your Axim and plugging it into a cheap card reader attached to your computer. There's no software to install, and the card will show up as a regular folder on your computer--you can simply drag and drop files between card and computer.
When you buy or download Windows Mobile (WM) software for your Axim, usually you get both a Windows installer that runs from a Windows computer and a WM installer that runs from the Axim itself. Since Mac users can't run the Windows installer, they simply copy the WM installer to the memory card (with the card reader or sync program; the WM installer is the file that ends in the extension ".cab" or ".CAB"; if there's more than one WM installer, choose the one with "ARM" in the name), then, with the card back in the Axim, use File Explorer to navigate to the card and tap the name of the installer. Done. Seriously--that's all there is to it: drag the installer file onto your card, put the card in the Axim, and tap the file name. However, one thing to think about is keeping your main memory free. Main memory is where the Axim does its processing--fill it up and the Axim doesn't have room to think. Thus if you're installing a large program, you should install it to a memory card rather than to the main memory. After putting the program's CAB installer file on the card and the card in the Axim, don't tap the installer's filename. Instead, tap the program cabinstl_en.exe on the SD card and use that program to install the CAB file to a memory card (if you didn't buy an Axim from me, you should search for, download, and copy cabinstl_en.exe to your PDA). All but three of the programs I've bought or downloaded so far have come with WM installers. Two of them, very small utilities, included only the WM program itself, no installer (filename ends in ".exe"). In that case, simply copy the file to your card, put the card in the Axim, use File Explorer to copy it, then navigate to the Program Files or Windows/Start Up folder, and paste the file into that folder. The other program, though, came only with a Windows installer (file ending in ".exe"--hint: if the .exe file is tiny–under 50KB, say–you can safely assume it's the program file itself; if it's much larger, then assume it's the Windows installer). If you have PocketMac, you can usually use it to extract the WM installer from the Windows installer--then copy the WM installer to the card, put the card in the Axim, and tap the installer file name. However, according to PocketMac, it's not always able to extract the WM installer. At that point you've got three options: