Yes, non-Muslim women should avoid Middle Eastern countries where women's rights are not recognized. Muslim women should also avoid these countries. There is no reason a country should take anti-women stances in the 21st century. We must make sure that all countries uphold the rights of all people in today's world.
There are many places that are not safe to travel to ad a woman or a man should discern whether or not the place they want to travel isn't so dangerous that they get killed or into trouble with the authorities. Through research they will have to find if people will welcome them and their customs.
No, women should not avoid countries where women's rights are not recognized. Women should, however, be aware of the lack of rights and other related laws before visiting these countries. If not comfortable with the country's views, women should avoid visiting the country at that point. However, women should travel anywhere they'd they to visit otherwise.
Although it is risky for women to visit these countries, I think this is a great way to speak out and raise awareness to the human rights violations that women are facing in these parts of the world. We need to help them to move forward and progress with human rights.