The degree with which a hijab is oppressive varies with the degree with which there is social pressure to wear it. In the US, it is not particularly oppressive. In many, if not all, Muslim majority countries, there is moderate to large amounts of social pressure for Muslim women to wear it (and in a number of Middle Eastern countries, pressure for all women and regulation for Muslim women).
It is also important to tie the practice to substantive oppression. American Muslim women, particularly those second generation and beyond, are not meaningfully more oppressed than the average American woman (which may be some, but certainly less than in the vast majority of the world). In other countries with large Muslim populations, the hijab is a component of broader social practices with are substantively oppressive (e.g. women can't drive, can't own property, etc).
It is interesting to compare it to wearing high heels, a practice which, if there were greater social pressure, would be very oppressive. Heels hobble movement and cause permanent damage to the feet, far more deleterious than the hijab itself (again, removed from the broader network of norms, see the above paragraph). I think pressure to wear heels, especially in a business setting, has decreased dramatically over the last decade and a half, as dress flats have become more accepted.