Actually, I think your issue is just an OK Cupid issue, not a big moral issue.
When you list your status as "Married" on OKC, you don't come up in people's searches unless they have expressly selected "Married" as one of the options for what/who they are looking for. You have the choice of being "Married," "Available," "Single," etc.
Choosing "Available," rather than "Single," might widen your options without causing outright lies.
Or, you could choose "Single" as your status to increase your "searchability" on the site, while also writing in your profile that you are married to a man but are looking to date women.
In general, I think it's okay to omit information on an Internet profile (for privacy reasons at the very least), but there are many opportunities to be truthful early on, when messaging someone, on a first date, on a second, etc.
As a less-morally-charged example, when I was using OKC last year, I listed myself as living in a big city an hour away from where I actually live. I did that so I could meet men in said city, because there were much fewer options in my home area. But I always came clean about my actual area of residence when chatting with someone, so they would know about the logistical difficulties.
And now I've got a great man who lives an hour and a half away from me