Why does Roark remain unconcerned and disinterested in the efforts of so many of the other characters to destroy his work and his career?
It occurs to me that there is another way to answer your question - and by using you as the example.
Imagine that you someday find yourself in a situation where things such as the fact that you support capitalism and not socialism, hang around Objectivist forums, enjoy certain types of unpopular music, etc. are considered disadvantages or impediments towards other people giving you opportunities necessary in order for you to pursue your career. Imagine when you are on your first job with a firm and you have colleagues who either dislike you or wish to eliminate the potential competition you might become in the way of their ambitions and they start a campaign of making it known to the higher-ups that you read Ayn Rand, spend your weekends doing World War II reenacting and do not participate in rock music /pop culture type stuff - and, as a result, despite the fact that you do outstanding work, the higher ups have an impression of you as an oddball and regard you as being “too eccentric” to be trusted with a promotion.
Would you be angry at the behavior of your colleagues - or would you, instead, feel something more along the lines of contempt and disgust?
The situation I described is similar to Roark’s in that efforts to destroy Roark’s career did not involve things such as slander or libel or some other form of force. All they did was attack him and attempt to destroy his career on grounds that Roark built certain types of buildings and had certain attitudes towards other people - all of which was, in fact, true. Had someone tried to destroy Roark’s career by spreading a rumor that he was a child molester, I am sure he would have been very angry and probably would have taken legal action if possible.
In my example above, your colleagues are attempting to destroy your career on grounds that you have certain beliefs and values which you openly and proudly admit to having. Assuming that they don’t resort to fraud or force, your primary complaint against your colleagues would be that they reject and despise your values and make that fact loudly known. Granted, that can be annoying and disgusting - but is it grounds to become angry or upset?
How can he sleep with a woman who openly is trying to destroy him, or accept a job from a Wynand who has sought to destroy his other jobs with his paper?
Dominique and Wynand both have unique contexts which have been mentioned in other postings.
I am sure if someone was trying to destroy my career I would be likely be more than a bit irate at them, or at least concerned as to trying to counter or stop their efforts and save my career.
I have no doubt that Roark wished that people such as Toohey and Keating and others did not exist in the first place and would simply go away. But what would he accomplish by becoming irate at them? And exactly what could he do to stop or counter their efforts? Become Peter Keating? That would stop the attacks pretty quickly - but at what price?
To go back to the hypothetical example I gave about your own career - what on earth could you do to counter or stop such efforts on the part of your colleagues? Claim everything they are saying about you is a lie and pretend to be a socialist? Resolve to give up your hobbies and go out clubbing with your colleagues and pretend to enjoy the rock music? If you did that, you might get a promotion - but what would be left of you and what enjoyment would you ever again be able to get out of life? This hits on the major theme of the entire novel.
In such a situation, the only option to save your career that is open to you as a person of self-esteem and integrity is to do what Roark did: seek out the better sorts of people who will deal with you on your terms - which, in this context, would consist of finding an employer who will judge and reward you based on what matters, i.e. how well you do your job. If you could not find such people in positions of authority in your current firm, then you would need to look elsewhere. In the long run, what would be the point of spending the time and energy getting upset over the behavior of fools and idiots? It is a much more productive to focus on finding ways to minimize the need to have to deal with such people in the first place.
A key passage about Roark’s mindset is in the very famous scene where Toohey asks Roark to tell him what he thinks of him. Roark’s answer: “But I don’t think of you.”