And the official line is that Grace Lee Whitney was let go because Kirk needed to play the field.
It's easy to overlook with all the focus on the Civil Rights movement that many people involved in the show fought in WWII, which was just over 20 years before.
I don't think it is possible to say that Takei is absolutely wrong even if we can say he isn't absolutely right.
Shatner was electric. Nimoy was alluring. McCoy's wore his heart on his sleeve. Of course Sulu couldn't compete with them, he was witty, but quite vanilla, but he complemented them. There was a definite intention for Uhura, Rand, and Sulu to have larger roles, as can be seen in the first half of season one. Kelly, Whitney, Doohan, and Takei were all guaranteed a minimum of 7 our of 13 appearances.
Sulu had some pretty meaty appearances in season one but not a focus episode and they did tail off. The exact reasons for reducing involvement overall are likely multifactorial and certainly not entirely down to Shatner's intervention but it is entirely possible that Shatner's behaviour was part of that culture shift.
Not every debate is is intended to be bad tempered. Not every discussion has to be polarised. There is no absolutely right or wrong answer. Takei is neither devil nor messiah, and neither is Shatner.
Although I have used the phrase, Shatner is a god, more than once to be fair.