In the West, there's an attitude of "if men can do it, so can women", and so the custom can come across as sexist (though I don't think it's any more sexist than the necessity for women to take special hygiene measures during their periods).
Its all blood. I walk out or don't go with small cuts, and I always stayed home with my wife unless I had an actually important role in something. Yes, but you're absolutely right that it is viewed as sexist. But that was never the original reason. Only the Brahmin priest is allowed in the moolasthanams, etc. so there has always been 'discrimination' and often for good reason.
Many of the customs have much deeper esoteric reasons. Take marriage for example. The Hindu wedding ceremony is rich in esoteric mysticism on many levels, starting with the presence of gold, and Agni (the fire) being the messenger deva to inform all other devas of the vows taken by these two souls. But these days people just run off and have a destination wedding amidst lots of music and booze.
So I'm a traditionalist. I like the old weddings, and understand on a very mystical (and experiential) level the reasons for such things. Let's just say, for the sake of brevity, that certain energies, somewhat angry, or perhaps mischievous can sneak in the back door and wreck havoc in the aura, the mind, and the vibration of the place, including homes and temples.
I've actually seen priests who knew the purity vibration had been broken, and then they had to work a few long extra hours to do special clean-up rites for several days. So its not fair to them either. This was at a major Indian temple, and they actually closed it for several days. Nobody at all allowed in.