Just want to provide some information before giving my recommendation -
Windows and Mac OS use different file systems (NTFS / HFS+) to store files. Therefore, Windows does not support HFS and Mac only partially supports NTFS (can only read, but not write). Therefore, having the drives formatted with NTFS is probably the way to go here, as you at least gain read support from Mac OS by default.
There is no official reason as to why this is the case, but the common assumption is that Mac OS doesn't support NTFS because it's not open sourced, so Apple can't officially implement it without licensing the technology.
So to the question - what can you do? You can use third party software to install a driver that enables writing to NTFS external drives. There are a few of them:
- Mirvago NTFS Mac Mounter
- Paragon NTFS
- Tuxera NTFS (I'm a new user so can't post more than 2 links - google it if you choose it)
All three are used by large enterprise companies and also for personal use, so you can be safe to assume they are great products.
There are also some free ones such as Mounty, but I wouldn't recommend them as they rely on the default hidden feature of Mac OS that allows to write NTFS, but this feature is in beta mode, which can cause corruptions and data loss.