It doesn't matter if the random_state is 0 or 1 or any other integer. What matters is that it should be set the same value, if you want to validate your processing over multiple runs of the code. By the way I have seen random_state=42 used in many official examples of scikit as well as elsewhere also.

random_state as the name suggests, is used for initializing the internal random number generator, which will decide the splitting of data into train and test indices in your case. In the documentation, it is stated that:

If random_state is None or np.random, then a randomly-initialized RandomState object is returned.

If random_state is an integer, then it is used to seed a new RandomState object.

If random_state is a RandomState object, then it is passed through.

This is to check and validate the data when running the code multiple times. Setting random_state a fixed value will guarantee that same sequence of random numbers are generated each time you run the code. And unless there is some other randomness present in the process, the results produced will be same as always. This helps in verifying the output.

If you don't mention the random_state in the code, then whenever you execute your code a new random value is generated and the train and test datasets would have different values each time.

However, if you use a particular value for random_state(random_state = 1 or any other value) everytime the result will be same,i.e, same values in train and test datasets.

when random_state set to an integer, train_test_split will return same results for each execution.

when random_state set to an None, train_test_split will return different results for each execution.

see below example:

from sklearn.model_selection import train_test_split

X_data = range(10)
y_data = range(10)

for i in range(5):
    X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, test_size = 0.3,random_state = 0) # zero or any other integer
    print(y_test)

print("*"*30)

for i in range(5): 
    X_train, X_test, y_train, y_test = train_test_split(X_data, y_data, test_size = 0.3,random_state = None)
    print(y_test)

Output:

[2, 8, 4]

[2, 8, 4]

[2, 8, 4]

[2, 8, 4]

[2, 8, 4]

[4, 7, 6]

[4, 3, 7]

[8, 1, 4]

[9, 5, 8]

[6, 4, 5]