I would have to say no, my husband and I would not be ok with it. We are each other's best friend. We understand each other better than ANYONE else, even family. We don't need a friendship outside of our marriage that would be that close with anyone, much less someone from the opposite sex. Sure we have friendships of the opposite sex at work, mutual friends etc. but not that close. Co workers are friends at work to talk to and our mutual friends we hang out with together. I would never be close to someone else of the opposite sex because I wouldn't really feel the need to, my husband is that person. He goes to the grocery store with me, I go to Lowe's with him. To be honest we both work a lot during the week so the limited time we do get to see each other is pretty much only on the weekends. I don't really have time for anyone else.
Having said that, your business is your business. If you are both ok with it then I say who cares what other people think? I would just be careful to make sure you aren't "emotionally" cheating like someone suggested. That can be a very slippery slope.
IMO - I wouldn't do it, but your relationship with your spouse is YOUR business. Don't live your life based on other people's judgmental attitudes