When resentment creeps in and your partner is unforgiving of past transgressions, when you are repeatedly told you make the other person "uncomfortable;" when virtually anything you say is either twisted and turned against you, or deemed "a lie," when you realize that your only value to the other comes in the form of $$; these might be an indication that the "relationship" is toxic. When the opposites of these things are true, you're probably doing OK, as long as you're communicating genuinely and respectfully with one another.

Right now I’m single, i.e., between dysfunctional relationships.

Communicate and be respectful.
Toxicity comes in all forms and, in some cases, depends on how it is received. 1 person might like having the door opened for them and another not so much.
As to what is real, not sure what that means. I thought my marriage was real until it wasn’t

Have been single for some time. The paramount key to any relationship regardless if it is romantic or platonic is communication.

Toxicity is harmful. Can you disagree without devolving into personal attacks? Yes = healthy, no = toxic. Does you partner belittle you or put you down in any way? Yes = toxic. Do you both feel safe to speak your mind even when you don't agree? A healthy relationship builds you up, a toxic one tears you down. I'm sure there are more perspectives on this issue, this is mine.

When you disagree on something and you try to come to some sort of compromise or fix. If it just turns into a contest you are trying to win, that is toxic. This is of course just one thing, but it is the first thing that struck me. You are suppose to be on the same team.

Well, we do not call it a relationship anymore... we met and dated 16 years ago. If we are in the vicinity, we seek and see each other. When we lived in different states, we visited each other. We had lived together and those who know us, see us as a couple. And nobody seems to break our flow. Once again several states between us. We no longer sleep together but dinner, movie, dancing, hang out continues for us when near each other. I left 5 days ago and today we were talking Lake Tahoe, Grand Canyon, Vegas, Reno, Hoover Dam, etc... I am easy to get along and loyal... her being a professional ballroom dancer makes me look like a million dollar dancer, that I am not. Companionship and sincerity... We are Real to each other but... me being a none believer and she very involved in her faith and church. Is that Wedge that keep us from dreaming about making it together. We can have anything from each other except a future. And we both accept our reality and we both support the other finding a better or more workable match.

I would say when your gut tells you that your partner is reaching out to you rather than running away. But hey i am no expert.

Mutual respect, support and admiration are some of the qualities that are a part of a healthy relationship. You won't always agree, but when both parties work toward acceptance of one another's differences in perspective/opinion, understand each other's strengths and find a way to compromise, you both can have balance in the relationship. Sometimes it means taking turns for both persons to 'get their way'.
Truthfulness is important too. That being said, truthfulness does not not mean saying what is on your mind or how you are feeling all the time. Knowing when to hold your tongue when you are about to say something derisive or to say what you are thinking, which might be vengeful or mean, is a good trait to develop for both parties.
Seek to understand. Ask open questions like "what do you think about..." or "how would you feel if..." or "help me to understand why (what, where, when...)". These questions that allow the partner to express what they think and feel, also provide information so you can zoom in on what is an underlying concern or issue.
If your partner ever calls you disparaging names, insults you, hits or manhandles you, in private or publicly, RUN, RUN, RUN! That person is TOXIC!