It's coopted the same way as leftism.

A nazi says to "secure" the borders, kill or arrest anyone who tries to get inside and expel anyone who is already here, a regular nationalist would say that making the borders hard to cross is just enough. A liberal would still favor these policies but to allow exceptions for people who might seem useful to the state or to companies in order to secure a spot in competing against other nations who all have the same ideas on how a state must be run and how everyone is a competitor to fight against.

Or if a nazi or nationalist says that climate change isn't real or that it's not caused by humans and thus nothing must be done by the state, a liberal will disagree. But will still do nothing as long as it's not profitable.

Not to mention that the more popular the far-right gets, the more likely a liberal is to adopt their positions out of sheer opportunism and to "win back voters".

Liberal politics are like quicksand, you can go and convince people all you want of how you should vote CDU to prevent the AfD from winning the county governor seat and you'll probably be successful - all it does it keep people within the logic that the main conflict is not between a state where private ownership of the means of production (i.e. owning a factory, a shop, etc. - hiring people, telling them what to do because you're their master boss, etc.) and the people which should free itself from looking down at each other because one is allowed to force you to do what you must do and how you must do it (and how you must act - raise children, work hard all your life, buy stuff, etc.), from being one bad day, injury, physical or mental inadequacy from being fired and forced into subsistence and depending either on your own survival skills or aid, from an economy where more must always become more+ and it will never stop lest a rich man drive another rich man into poverty even if it kills the planet, etc.

Instead, a liberal will tell you that what REALLY matters is the conflict whether you're allowed to be discriminated against as for example a woman, because it will keep an economic advantage for the man, or if that's bad because working and richer women = more sales, more profits (it does the economy good), and packaging it all in moral sin-and-virtue wrapping. It might bring you short time relief (until the circumstances change and for the women example the population starts dropping, so even libs will want women to have more children for example) , but will never get rid of the underlying problem.