I don't get the "either/or" mentality. It's perfectly normal to film two things at once and enjoy them both. Easy for Takei to support TOS even while on other projects. One experience doesn't detract from the other.
Exactly. Unless you're a series regular (which, remember, Takei wasn't), you can't make a living as an actor without taking multiple jobs. It's common for recurring cast members on one series to take gigs on other series during its run.
In fact, let me research that -- other acting jobs by TOS main cast during TOS's run.
Shatner:
Gunsmoke episode "Quaker Girl"; movie
White Comanche;
CBS Playhouse episode "Shadow Game"; TV movie
The Skirts of Happy Chance.
Nimoy, Kelley: None I can find.
Doohan:
Iron Horse premiere episode "Rail Runs West";
Jericho (1966) episode "Eric the Redhead"; movie
Jigsaw. (IMDb also credits him playing a recurring chauffeur on
Peyton Place at the time, but Wikipedia seems to say he only played the role before TOS and the character was then recast.)
Nichols:
Tarzan 2-parter "The Deadly Silence"; movie
Doctor, You've Got to Be Kidding!
Takei:
Mission: Impossible episode "The Carriers";
Felony Squad episode "A Blueprint for Dying"; movies
The Big Mouth and
The Green Berets;
It Takes a Thief episode "To Catch a Roaring Lion."
Koenig:
Mannix episode "Delayed Action."
Barrett:
Please Don't Eat the Daisies episode "Just While You're Resting"; movies
A Guide for the Married Man and
Track of Thunder;
The Second Hundred Years episode "Remember the Maine";
Here Come the Brides episode "Lovers and Wanderers."
Okay, so Takei did more guest appearances elsewhere than most. But considering how few Asian-American actors there were in the business at the time, it stands to reason that each of them would've been in fairly heavy demand.