'People' ? Muslim people are not people now ?
What? Muslim women aren't safe in Muslim countries, either. Not in extremist Muslim countries, of which Egypt is one. I can't think of a single Muslim country that has a separation of state and religion right now, and where women can live safely. Not to say that there is none, but I can't think of one right now.
So, yes, I would ask why a Muslim woman would want to go to Egypt, too, if it was just for a holiday and not for visiting family.
Nothing to do with religion as such - I also wouldn't go to Brazil. If you hate women, you won't get my money. Simple as that. Not so sure I will go to Ireland again; when I was there first I didn't know just how much the government hates women.
If you want to support a poor country that needs tourists, why not go to Greece?