Why should I avoid having differents filesystem for / and /home?

I think @AndroidDev is right, it's just about unix file permissions that can't be saved in FAT{12,16,32}, or exFAT and hardly in NTFS. The author clearly had the standard example of a Windows user switching to Ubuntu in mind, see the last section of the wiki page. Btw, see this question for a discussion about the quality of your linked wiki.

tl;dr: Mixing file system in your installation should be no problem as long as they are all suitable for Linux, i. e. support file system permissions as well as symbolic links. In general this means every filesystem is fine except FAT and NTFS.

(source (German))