Is transhumanism inevitable part of any modern science fiction set in The Future (and aiming for at least moderate plausibility)?
No. There are plenty of ways that humanity's future might not see this kind of progression, or at least not in the context of a given setting and group of characters. The simplest and most extreme example is post-apocalyptic fiction, where mankind's ability to wage science is hindered or eradicated by some kind of cataclysm, be it man-made or natural. Or, you could assume your sci-fi novel is a cautionary tale against the growing trend toward anti-intellectualism and anti-science in certain parts of society.
Anyway, I think you could get there if you wanted.
I actually haven't seen much transhumanism in sci-fi set within a reasonable time frame (no later than 2500AD, anything else it too far in the future to be anywhere near believable). As for my setting(2335 and not very advanced for it) there is very little augmentation in common society due to costs and regulation. The most upgraded someone, other than a severe trauma victim, would be implanted neural networking to electronics as the civilian populous either doesn't have a need for or the funds for much else.
It seems unlikely to me that advanced medical technologies would remain financially unavailable to the common population hundreds of years in the future. Moreover, in an interstellar society spanning several star systems (or even just our own Solar System), regulating human enhancement technologies everywhere would be pretty much impossible.
As for really far future stories... Even they can be realistic, plausible and internally consistent. Are you familiar with the Orion's Arm universe project, for example? I find the fictional, ultra-transhumanist universe (set over ten thousand years to the future) it portrays to be far more interesting and realistic than most "mainstream" scifi universes.
There needs to be a line drawn between lifesaving medical technology and non-essential augmentation. The US government in this setting could give the USSR a run for their money in totalitarianism. Each colony (there's only a handful of earth-like planets that can actually support earth-borne life) is controlled by a an elected local government(ballots prepicked by the administration) which has its tentacles in almost every aspect of life, especially the healthcare system because of how fragile society is in a near-famine disease ridden environment.
And sorry, no. Nothing set more than a thousand years in the future is ever going to be read by me. It is too infinitely unpredictable, imagine trying to predict our present from 1000AD.
It's entirely possible, even if the end result is not even close to what we will actually have by the time we get there. It'd be foolish to limit yourself with such extermes as "I will never do X"... At least the Orion's Arm universe is strange enough - much, much stranger than our modern world would be to cavemen of 10 000 years past.
Sorry brah, ain't gonna happen. Far future fiction always reads like cheap high fantasy to me; unbelievable, crude, and arrogant with a unhealthy dose of the author's favorite aesops about whatever over optimistic crap they think'll get their feeble message across.