Whoops. When I read the title I thought this was about when your spouse is having affairs because they keep forgetting they're married.
I have seen Alzheimers close-up and it is a very cruel disease. The frustration and sadness of the family of sufferers is intense. Caring for a spouse or family member who does not recognise you or remember how to do everyday things (like drink a cup of tea or get dressed) is very draining.
I don't think I could be too judgmental of someone who seeks other support and companionship after their spouse has a complete mental break. I imagine there would be legal issues with trying to divorce someone who does not recognise the implications of the contract.
It should be a situation discussed early in your marriage. If I developed Alzheimers or an incapacitating illness and my spouse wanted to care for me but also have a companion, I think that would be all right.