Is it true that a big part of the kh fanbase ship soriku and dislike kairi?

It's a vocal minority.

It's true that many idiotic fangirls (no offense intended to those who now probably want me dead) ship it simply because they want to, yaoi and all that. And yes, Kairi is caught in the crossfire simply for being Sora's girlfriend.

But not every KH fan is a girl. Not every girl is into yaoi. Not every yaoi fan will do this. There are people who insult and deprave the series with this stuff but I can assure you that the larger portion of the fanbase are perfectly sensible.

Some do.Some don't .Simple.

There are quite a lot of Soriku, not sure about the Kairi thing though.

Yes.  And because Kairi is portrayed as Sora's love interest, those who do ship SoRiku detest her for "getting in the way of Riku and Sora's awesome sexy times".  But as said, not every yaio fangirl does this to the pair.  The ones that do just make sure the whole internet hears.  

On the topic of Kairi, I just realized how much of KH2 was completely about progressing the interest between Sora and Kairi. Donald and Goofy were always teasing Sora about Kairi and just about every world that had romance in it held a scene about Sora thinking about Kairi in a way that filled out that love interest.

Big part? Nope. I'm sure most Kingdom Hearters ship the one true otp, SoKai.

I ship Soqua.