Afaik we are not able to read thoughts let alone regulate them (not even for ourselves). So this whole statement is kind of a straw man, as it's not about "thoughts" it's about speech and action following from that. At least that is what the paradox of tolerance is concerned with, so why else would you mention it?
Also obviously the paradox of tolerance is biased in that it asserts that a "liberal, pluralistic society", one in which everyone is able to express themselves, is a good thing. So it rejects ideas of authoritarianism and totalitarianism which would argue that the will of the authority or a certain ideology is to be followed dogmatically.
That's not a some hidden agenda that's the plain and obvious premise. The paradox is whether you should accept people who challenge that very premise. Because if you allow for people to silence others and submit them to their will, then you're freedom to express yourself is gone. However if you overdo it you'll be the one silencing and submitting people to your will. That's the paradox. So despite having the intent to be tolerant you need some intolerance towards the intolerance to enable a tolerant society.
Now intolerance doesn't have that paradox. Intolerance simply doesn't care what other people have to say, what their perspectives are and whether they are able to express themselves and contribute to the public discussion. Intolerance specifically means that you "do not allow/accept" it, so it favors that there is no discussion and that people just take up their place in the Intolerant's master plan. So for the intolerant it might just matter whether they are in power to command others or whether they are subject to someone else who commands them. Silencing and subjugating other's is (to the intolerant) not a contradiction with their goal, it IS the goal.
Everything originates from unique thought, so therefore such thoughts
are naturally non-constrained.
That's not really a sound argument. First of all not everything originates from thoughts and thoughts might themselves originate from experience and whatnot. And even if they did why would that mean that they are not constraint?
Even if some ideas would be harmful, there cannot be a general
consensus on appropriate emotions.
There can absolutely be a consensus on appropriate emotions, why shouldn't there be one? Whether that's any useful, whether you're able to control your emotions to that extend, whether it's enforceable or whether that's a good idea to begin with. Would all be valid questions about such ideas but that doesn't mean you couldn't do it.
Feeling low in self-esteem is not a
problem, since nature does not guarantee some certain level of esteem.
A problem to whom? To you who might not feel that way? Maybe, maybe not. Do you care about that person with low self-esteem and don't like to see them struggle? Then yes it is a problem. If you don't well, that's up to you. But to the person having low self-esteem that most likely is a problem if it means they don't enjoy being themselves. And what does nature have to do with that? Is nature any normative in that sense? People aren't naturally meant to drive, fly have computers or whatnot and we do it anyway, so why should we constrain ourselves to what is natural? It's not like everything there is in nature is by default good, there's death, harm, suffering and whatnot.
There's a limit to that thinking in terms of pissing in the pool that you're swimming in (climate change, pollution, questionable industrial production of food optimized for profit not health, and so on), but that doesn't mean we have to feel bad because it's "natural". On doesn't have to accept a status quo especially not if it isn't working to begin with.
One caveat to the nature of ideas: Sure you might not be able to control the onset of emotions. Like if you're feeling sad, angry, happy or whatnot you're feeling that regardless of whether you want to or not and there's hardly anything you can do about that. But how you deal with those emotions is still at least partially up to you. And you can argue that certain ways of handling them work better or not as good as others.
In a more general sense, all ideas are arbitrary, since they originate from subjects.
That doesn't make them arbitrary... That just means you have to figure in a lot more individual context than you'd need to if you'd consider them to be subject independent or objective.
Based on this, racist ideas cannot be generally non-tolerable, because they're essentially a similar bias as any other idea and their interpretation as emotions is entirely subjective.
That depends on how broad you define racism here. Like whether you find someone likeable or abhorrent on first sight and based on a subconscious cocktails of whatnot is an emotion and/or bias. To construct a theoretical and practical ideology and engaging in political action with the goal to privilege your peer-group and/or disenfranchise another "group" (that might just be a group because you said they are), is a little more than a fluke of an emotion...
It's possible of course that racist ideas become false generalizations, but if they're ideas then they should be tolerated on the same grounds as "religious hocus pocus". Therefore one cannot claim that there's bannable speech without being favorable of protecting a particular set of emotions as more valid.
Why should you tolerate "religious hocus pocus"? I mean that's usually why you have a separation of church and state because you can hardly argue with religious people as their "god said so"-argument works for them and for nobody else, so there's no rational discussion. Which is why you make laws that are not based in religion and make religious people figure out how they can exist within these laws if they want to. Cults are literally one of these totalitarian groups which are intolerant and "unreasonable" as their acting upon axioms that may be false but are unquestionable.
I guess there's some level of variability in expression though, but
banning "inconvenient opinion" in place of "favorable opinion" is
opinion totalitarianism.
It's not about "different" or "inconvenient" opinion it's about the very foundation of a society and the kind of society you want to live in. Again societies are never unbiased and don't claim to. Modern societies explicitly fancy themselves for having equal rights, individual freedom, equality before the law, the ability to go into politics yourself or at least to elect politicians, equal suffrage and so on.
These aren't neutral, but these are fundamental to society as we know it. So if you try to chop away at those by making certain groups of people more privileged than others then you're eroding that very concept of society. It's not that this is a physical force or something that is impossible to do. But if you'd take Kant's perspective of the categorical imperative and envision yourself at the receiving end of such a system that strips people of their rights, freedoms and maybe even their lives then that's certainly not "good".
Also it might not even be all that great if you're not at the receiving end, but that's a different story for a different time.
TL;DR you can't just swap terminology these ideas are based on different premises