It’s noteworthy that the status of woman in Islam constitutes no problem. Many verses of the Qur’an and practices of the early Muslims bear witness to the fact that woman is, at least, as vital to life as man is, and that she is not inferior to man in any way. Islam never belittles woman or underestimates her role in the society. Allah has made this clear in the Glorious Qur’an, by stating shining examples of some women for the believers– male and female- to emulate. In this context, the Glorious Qur’an says, (And Allah citeth an example for those who believe: the wife of Pharaoh when she said: My Lord! Build for me a home with thee in the Garden, and deliver me from Pharaoh and his work, and deliver me from evil doing folk; and Mary, daughter of Imran, whose body was chaste, therefor We breathed therein something of Our Spirit. And she put faith in the words of her Lord and His Scriptures, and was of the obedient.) (At-Tahrim 66: 11-12)
Thus, as the regards the point you raised in your question, we’d like to make it clear that the Hadith does not depict a woman as inferior; not at all. As it’s a fact that man has been given a form and nature by Allah which is distinct from that of woman, it’s also a fact that the form and nature of man and woman is complementary. This indicates that the distinction in form and nature must not be equated with an intellectual pre-eminence on the part of man.
Based on this, we’d like to stress that the issue of having a woman’s testimony corroborated by another woman does not imply a sign of gender superiority. One will get this point clear by bearing in mind that shyness is a specific feature of woman as compared to man. In this case, she needs another woman to stand by her side and corroborate the evidence. There is nothing wrong with having a witness’s testimony corroborated by another witness if the statement of the former falls short of being admissible as a conclusive evidence. So, the main issue here is how to make justice run its course.
Focusing more on the question in point, we’d like to cite the following Fatwa issued by the late Muslim scholar, Sheikh `Abdul-`Aziz Ibn Baz, the former Mufti of Saudi Arabia:

The Prophet, peace be and blessings upon him, explained that women’s mental deficiency is reflected in their weak memory, the fact that makes Shari`ah stipulate that a woman’s testimony must be corroborated by another woman. Thus, this injunction does not imply woman’s inferiority to man; rather it has more to do with justice than to gender.
As for the shortcoming in religion, this stems from the fact that when menstruating or having post- partum bleeding, women neither pray nor fast, and they do not have to make up for their prayers.
As we know, women have no hand in the obstacles that disrupt their religious performances. This is something divine, which reflects Almighty Allah’s overflowing mercy on them, for it will be extremely hard for a woman to be tasked with religious obligation while she is having menstruation or post-partum bleeding. That’s why she is exempted from fasting or praying, as a sign of mercy on her. Also, they do not make up their prayers. This is because if they were ordered to make up their prayers, it would be extremely hard for them, given that prayers are performed five times a day. Menses may last for a number of days, up to seven or eight or more. Post-partum bleeding lasts for forty days. It’d be definitely hard for women to be obliged to make up the prayers missed while responding to the demands of nature.
So, in the light of the above-mentioned facts, the Hadith does not have any indication of looking down upon women or considering them as inferior, especially when we know that some women excel men in many matters.
Yes, no one can deny the fact that a woman may perform many good deeds and exceed many men in virtue, morality, etc. Islamic history abounds with examples of great women who have made great contribution to the progress of mankind. This is very clear to anyone who is well informed about the status of women during the time of the Prophet, peace and blessings be upon him, and the early generations.
In addition, the Hadith in question does not disqualify women from being narrators of Hadiths, and there is nothing that prevents a woman from being one of Allah’s pious servants, if she is steadfast in her religion even with her being excused from fasting or praying during menstruation or post-partum bleeding.