Will an algorithm that constantly changes the order of 10 hash functions be protected from an ASIC? Let's imagine one hash function that is based on 10 hash functions. For every input, it changes the order of the 10 hash functions. So, for example:
Hello, World! -&gt; md5 -&gt; sha256 -&gt; sha512 -&gt; sha3_256 ... -&gt; resulted hash -&gt; sha256 (additionally)
Hello, World? -&gt; shake_256 -&gt; md5 -&gt; sha256 -&gt; sha3_256 ... -&gt; resulted hash -&gt; sha256 (additionally)
Will it be impossible to create an ASIC for such an algorithm? And if yes, what would be effective for brute force?
Will it be impossible to create ASIC for such algorithm?

No, actually it is quite easy.
The way you'd design a single brute-force core then is that you take a hashing engine for each hash function used, an input generator, a hash validator and a smart interconnect.
Then when you want to brute-force an invocation of ordering 1, the input generator outputs the guess along with routing / ordering information for the interconnect which then sends it to the appropriate engines in the appropriate order. As you are only targeting one ordering at a time, you could possibly even make this a state register of the interconnect. Then, once the first engine has processed the first piece of data, the interconnect receives it back, checks its ordering register and sends it to the next engine, while accepting the next guess for that ordering from the input generator which is promptly sent to the first engine.

Will it be impossible to create ASIC for such algorithm?

As you have seen exemplified above, there is no algorithm which is really hard to brute-force for an ASIC. The best one could hope for is that the optimal ASIC configuration would be (close) that of a modern CPU, but even then, chances are that the algorithm will not use specific parts of the CPU, e.g. FP cores, which a dedicated ASIC can drop.