You snooped or stumbled across evidence your partner has been doing some things they shouldn’t online. You know what you know and you can’t un-know it. Social script dictates that knowing this information, you should righteously flail about spilling piss and vitriol. Instead of behaving like a spiteful demon, why not actually address the problem like an adult.
Instead of flying off the handle, use this as a moment to talk to your partner about their desires. Normally when this sort of thing happens it’s just your partner’s way of expressing their sexuality or affirming themselves. Sure the temptation for infidelity is there but there’s no way for them to fuck accidentally over the internet.
In terms of violations, chatting with people on adult dating websites and the like is pretty tame. It’s almost exactly like what I would do in AOL chat rooms as a kid. It’s play, fun and usually completely innocent. These people will probably never interact in real life but in the virtual world they can get the affirmation and stimulation they crave without actually risking much if anything.
Despite how relatively safe and innocent the activity is, it’s still perfectly understandable to feel betrayed or hurt if they kept it from you. No matter how much you try to apply reason, you’re still going to feel it and you don’t have to hide it or feel bad. You should, however, recognize that this violation doesn’t have to be an extinction level event.
If it bothers you so much that you’d be willing to throw away an otherwise fulfilling relationship, that’s something that needs to be addressed. That sort of leveling reaction to relatively minor infractions speaks to larger issues in the foundation of the relationship. No digital person should ever make you feel like your relationship is at risk.
If it’s your partner’s behavior that’s making you feel uncomfortable, discuss it. If the entire idea makes you sick, discuss that too. Talking about the behavior and how it can fit in your relationship, will bring you to some creative, personal solutions, like you becoming their anonymous online kinky pen pal.