Cheating is not polyamory. It's cheating, period.
Cheating requires hiding and lying, which makes it unethical, while one major aspect of polyamory is the full knowledge and consent of everyone involved, and that makes poly ethical.
It's a shame that your partner feels it should be acceptable to you that they are deceptive and dishonest in his or her relationships. That kind of terrible betrayal can be a deep wound that causes irreparable damage to people's lives. It isn't only about your neighbor and the awfulness being done to their partner - it means you will also have to live with the lying and sliminess of it all (even if you and your partner don't live together), and who needs that kind of energy around them all the time? Ecch, it will feel like the crud and mess your partner creates in that entanglement will rub off on you and make you feel as dirty and dishonest as he or she is being. That is not a nice thing to do to you. Besides, if your partner is okay with such dishonesty with this other person, how can you be sure they will ever be honest with you?
From the statement you made about having had to deal with infidelity in your relationship, it sounds like your partner has had a history of dishonesty with you, and you were hoping poly could be a way to heal from that. I would say that unless your partner is willing to examine this need they have to be covert and dishonest, and to dig deep into the underlying issues about that, he or she is definitely NOT ready to embrace polyamory AT ALL. Some couples take a year or two discussing and examining and dealing with deep issues like this before opening up their relationship to having others, simply because doing so helps to build a strong, honest foundation. And a strong relationship that really works well, one in which the partners are willing to shine a bright light into the darkest corners where fears and insecurities and old belief systems reside, is what is needed to practice polyamory.
Some poly relationships start with cheating and there is a possibility that they can succeed after everyone comes clean, deals with the betrayal, and the cheaters rebuild trust again, but it is an extremely hard and gut-wrenching road to take. It is unkind of your partner to push his/her agenda on you and say that you need to change your thinking about it and be more accepting. That is hogwash. You don't approve and you don't have to. You can't stop your partner from behaving like a shit, but you can draw the line about what you will tolerate. Do you stay with a cheater? Do you keep their secrets? These are questions you need to ask yourself and confront your partner about. Maybe after a few more responses, you can invite your partner to read this thread for some other, eye-opening perspectives.
I am sorry you've been put in this situation.