As to Takei, he's hardly the only one who had issues with Shatner - Nichelle Nichols is quite famous for her distaste of the man.
James Doohan hated him too. Really, it's hard to find a TOS actor who actually got along with Shatner.
Takei, Nichols and Doohan all vastly overestimated their importance primarily because during the 70s fans started to blow sugar up their asses and treated them like Trek royalty, that was when the myth of the crew as a family started and Shatners only crime was that during the production of the show he didn't treat them like equals, which they weren't!
I think many people often forget that TOS was not an ensemble show, its main cast consisted of Shatner and Nimoy in the first season, Kelley got a promotion for the second season. That's it, three main characters with Shatner being the star of the show.
If I remember correctly James Doohan and Grace Lee Whitney actually got contracts for a number of episodes (not all of them though) but Takei and Nichols were dayplayers, if they were available they appeared on the show, if they had another job that week a random actor was put in their seat and got their lines, that's how important they were i.e. not very much if no one bothered to secure their availability.
Out of them Grace Lee Whitney was acrually the one who got screwed over (not by Shatner though), Rand was originally supposed to have a bigger part, she even appeared in early promo pictures with Shatner and Nimoy (waering pants!).
Shatner acted like the star of the show and didn't really give them the time of the day, so what? I don't even remember him ever saying a bad word about them, his stanced always seemed to be "I barely knew them, they were there on some days and not on others", the feud seems to be completely one sided and I'm ready for Takei and Nichols to shut the fuck up, it was not Shatner's mission to ruin their time on Star Trek and considering they're still making money with convention appearances decades later it wasn't such a bad deal.
Walter Koenig was in the same position but he's not part of the bash Shatner club. He made some comments and of course Shatner wasn't perfect (nobody is) but he generally seems to appreciate his time on the show and the opportunities he got out of it.