I'm surprised no one's mentioned a while loop yet:

    start = 0
    while (end := my_str.find("x", start)) != -1:
        print(my_str[start:end])
        start = end + 1

vs

    start = 0
    while True:
        end = my_str.find("x", start)
        if end == -1:
            break
        print(my_str[start:end])
        start = end + 1

I'm still on the fence myself so I sympathise with your view, but the first version is certainly a bit tidier in this case.