I wonder if Westerners are accepted at these places?
As with all things in Japan, it depends. Westerners will be allowed in if they satisfy the requirements posted on the wall at the reception area. In most cases, anyone with tattoos will be barred entry (since tattoos == yakuza in japan).
Also, most capsule hotels are exclusively for men because it reduces the risk of rape (versus co-ed). There are one or two capsule hotels in Tokyo that I could find that are exclusively for women, but since the whole point of a capsule hotel is to provide a place for a salaryman (read: regular joe schmoe employee) to catch some sleep after a night of drinking and missing his last train home, it doesn't often happen that a woman would *need* to stay in a capsule hotel. Especially since Japanese society still largely encourages women to abandon their careers once they have children. And, as we all know, Japanese women are expected to be baby making machines , so *not* having children isn't really seen as an option.
Disclaimer: I lived in (albeit rural) Japan from 2005-2007, and I'm female. I looked for capsule hotels when I was there, and there were few that would accept me. My views on women's rights and societal expectations in Japan may be somewhat biased by my small-town life there, as even in Canada small-town women get exposed to fewer options and seemingly have fewer acceptable life choices than those in major cities.
Reality must take precedence over public relations, for Mother Nature cannot be fooled. -- R.P. Feynman