Yes, You Can Cheat When You're Poly
When people think of the word "cheating", they instantly assume that a person is having sex with someone that is not their partner. In fact, many people assume that polyamory is just a nice name for cheating. This couldn't be further from the truth.
Polyamory is, in short, consensual, ethical, and responsible non-monogamy. This goes directly against the idea of cheating. Cheating is non-consensual, in that the person being cheated on did not consent to non-monogamy, and is unable to make informed decisions about their sexual and emotional health. Cheating is not ethical; after all, a great many cultures and belief systems consider it the one of the biggest betrayals you can commit. And cheating is most definitely not a responsible thing to do.
I would go so far as to say that cheating is worse in a polyamorous relationship than a monogamous one. While it is still a horrible thing to do in a monogamous relationship, to cheat in polyamory is somewhat bizarre - you have an opportunity to be open in multiple ways, and the option to discuss and renegotiate the relationships, and yet you choose to do something outside of those options, something you agreed not to do.
Cheating is Breaking Rules...
I have known people that have done utterly baffling things when it comes to polyamory and cheating. A friend of mine had a rule with her boyfriend that they could each only date people of the same sex, and yet he cheated on her with another woman. This could have been renegotiated before he slept with the other woman and it would have solved the cheating problem.
A very common rule is a "one penis policy" or OPP, where an established couple, generally between a heterosexual man and bisexual woman, opens up the relationship, where both the man and the woman in that relationship can date other woman, but the woman is not allowed to date other men. While this sort of agreement can be all sorts of problematic, the point is that this agreement was made, and should be kept if you agree to it. If the woman has sex with another man, that is cheating in this relationship, and her partner has every right to feel betrayed.
The definition of cheating is a conversation every person should have in every relationship they're in, including monogamous ones. Cheating doesn't simply mean that someone is having sex with someone that is not their partner. What it comes down to is that cheating is breaking your relationship agreement. For many relationships, monogamy is part of that agreement, and so having sex with someone else is in fact cheating. But even there, there's a lot of grey area. Some people consider flirting to be cheating, some may be totally fine with their partners cuddling with other people without kissing, and still others may be okay with kissing but not with cuddling. And in polyamory, there's an even wider range of things that can be fine or off limits.
Some relationships have more rules than others, and some people have more boundaries than others. The important part, for any relationship and any topic, is to know the boundaries of everyone involved, and if there are any rules, make sure they aren't unspoken ones. Once you know what boundaries you're working within, you will know if you cross any lines. Conversely, if you make your boundaries clear, you can trust that your partner will be able to work within them.
...But Rules Can Change
If you are unable to agree on rules or accept someone's boundaries (for example, if you want to be able to spend the night at a partner's place, but a different partner wants to set the rule of no overnights with them), then there are really only two options: continue discussing the topic and eventually coming to a compromise, or eventually realizing that your wants and needs simply cannot match up, and maybe the relationship is something that would be better off coming to an end.
If you are able to reach an agreement on rules or boundaries, there's a very simple way forward. Once your boundaries are laid out, and any rules (if you choose to have them in your relationship) are set, you know what your relationship is like, and you know what you have to do to avoid cheating. Just don't break those rules or cross those boundaries.
Relationships change over time, and at some point, you may feel as though the agreement you set up no longer works for you. In that case, it's perfectly natural to renegotiate! People change, needs change, and self-realization changes. Maybe you weren't comfortable with a partner going on dates without letting you know beforehand, but now it's something you're equipped to handle. Maybe the topic of fluid-bonding with a partner comes up - restricting who can have unprotected sex is an extremely common rule (though it makes much more sense to state that you will only have unprotected sex with certain people, or only if they don't have unprotected sex with someone else, instead of saying that a partner is not allowed to. This allows for a much easier dialog if the topic needs to come up again, but this was covered in another article).
It's important to note that it is never okay to impose a relationship agreement on another person. Whether you have a set of rules that you'll place on a new partner without them having a say in it, or if you are an established couple or more-some and wish to bring a new person into your polycule, each and every relationship needs to have a discussion on boundaries and rules. It's especially important to note that, by the definition of "each and every relationship", you have to consider that each relationship between people needs to be discussed separately.
For example, if you are married and both of you want to date a woman, the discussion is not "the couple's boundaries and rules versus the woman's boundaries and rules" but instead it is four discussions. You need to discuss boundaries and rules with your spouse, of course, but you also need to discuss your relationship and boundaries with the new partner, your spouse needs to discuss their relationships and boundaries with the new partner, and all three of you need to discuss boundaries and rules that work with the entire group. It gets complex, for sure, but it is the only way to make sure that everything is clear, and everyone has a fair say in what they are okay with.
All in all, it is on you to create a relationship agreement that is workable for everyone involved. If you no longer believe that you can live within that agreement, don't cheat. Discuss, negotiate, and revisit the agreement, but in the end, if you're unable to find a compromise, it is so much better to live with those restrictions or part ways than it is to cheat.