While the ActiveSync software that comes with the PDA is Windows-only, the PDA itself will work perfectly well with a Mac. You do NOT need ActiveSync to transfer files (movies, photos, music, etc.) between your Mac and PDA, nor do you need it to install software to your PDA.
The main thing ActiveSync does is synchronizing frequently changing data between certain programs on your PDA and your computer--and you can get free Mac software that will do that, too, as well as let you transfer files between Mac and PDA over the included USB cable. For the most part, this means that, when you add or modify a calendar entry on your PDA, the same change is made in the calendar program on your computer, or vice versa. Ditto an address book entry or a note (syncing notes may require the paid version of the program). I don't recommend syncing email or browser bookmarks/favorites--that can quickly fill the Axim's memory and cause problems--but you can of course access webmail (gmail, yahoo, hotmail, etc.) through the Axim without any problem. If you don't care about keeping the same calendar, address book, and notes on your PDA and computer, you don't need to sync at all. If you want to try a different sync program, there are two other companies making products you can use, Missing Sync and PocketMac. 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 PDA in its cradle or on a sync/charge cable and then open up the PDA 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 at all--and do it much faster--simply by taking a memory card out of your PDA and plugging it into a 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. Remember to drag the card folder on the desktop into the trash and wait a few seconds before physically removing the card from the card reader; otherwise you may destroy the card. If your Mac has Wi-Fi, you can also transfer data (including program installers) wirelessly--see here for details.
When you buy or download Windows Mobile (WM) software for your PDA, usually you get both a Windows installer that runs from a Windows computer and a WM installer that runs from the PDA 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 stick the memory card back in the PDA.
However, one thing to think about is keeping your main memory free. Main memory is where the PDA does its processing--fill it up and the PDA 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. With the X51V, you'll automatically be given this option whenver you install a program. With the Japanese OS system or the old WM2003SE English system, tap the program cabinstl_en.exe in the Backup Files folder on the SD card and use that program to install the CAB file to a memory card (if you didn't buy a PDA 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 PDA, use File Explorer to copy it, then navigate to the Program Files folder and paste the file into that folder. The other program, though, came only with a Windows installer (file also 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, then even if the program comes with only a Windows installer, you can usually use PocketMac to extract the WM installer from the Windows installer--then copy the WM installer to the card, put the card in the PDA, etc. See the PocketMac documentation for instuctions on how to do that. However, according to PocketMac, it's not always able to extract the WM installer. At that point you've got three options: