I tag my mp3's with Windows Media Player (which uses the allmusic.com database). I'm pretty sure they affect the ID3v1 tag because when I host these mp3's onto a linux machine, the fields are shorten to 30chars. When I load these files in foobar, foobar reads the tags normally. I'm really confused on the issue and I want to know how to prevent the tags from being shortened.

ID3v1 has the 30 character limitation, ID3v2 does not. The files probably contain both versions of tags (which foobar2000 can verify). The answer might just be a matter of making sure you are using software that reads v2 tags, and/or setting the software to make v2 tags take precedence.

I was wondering, I first tag with WMP and then with foobar. Does foobar get rid of WMP's tag and use its own which only it can read?

foobar does what you make it to do.
there is no things like WMP tag in case of mp3, and no foobar's own tag at all.
there are common tag standards like id3v1 id3v2 and other

I would go with what sn0wman says above. However, be advised that foobar might delete some non-standard tags.

Not quite. When you generate tags with foobar 0.9.x, it will rewrite the existing id3v2 tag with an id3v2.4 tag which WMP will ignore. WMP will only read the id3v1 tag. From WMP's perspective, the id3v2.4 tag that foobar rewrites is "foobar's own tag". WMP is a well-disseminated music player from a huge corporation with deep pockets...that can't conform to a simple standard.

Your best bet is to use a tag editor like MP3Tag and configure it to write id3v2.3 tags and (possibly) id3v1 tags. You can figure out exactly what WMP is reading by making a small change to an id3v1 tag and seeing what WMP reports.