I am open minded enough to listen to some of the questionable things my friends believe, and then I do research and really try to see some real benefit, truth, proof, etc., but I am usually convinced by my research that it is bunk. Therefore my pat answer to some of these ideas is that if believing such makes them happy or feel better, then so be it, and it's likely true for the, but don't push those ideas on others or ridicule me for not believing.

Believing due to a gut feeling is ok, basing your actions and trying to force other peoples action (or gov actions) on this belief is a narrow mind.
Open mind is challenging your own beliefs and not challenging others on theirs.
An open minded ufo believer, would go around investigating claims that he believe by feeling but wants to discover and understand the real facts.
But what we see is people telling that they are open minded for believing and telling that you are narrow minded because you refuse to accept a claim without some good evidence.

I think and trust that you will find that the most open-minded people on this insignificant hunk of rock we call the Earth would the declared Atheists since we, for the most part, have read and studied the Goat-Herders Guide to Galaxy word by word, line by line, chapter by chapter, etc, etc, WITH an open mind and not, as ever so many Faithfools do, merely Cherry-picking our way through it.
That also covers how we, Atheists view Science, History, etc, etc, i.e. we read it, digest it, dissect it, examine it, weigh it up and then, also with an open mind, come to our own conclusions, theories, etc.
To me, personally, having an open mind is where ones is OPEN to see both sides of everything equally, understanding both sides equally, examining it from ALL sides equally, etc, and then and only then forming your own conclusions, etc.

I agree. I'm open minded but still have a brain.

I define being "open minded" differently. I am but depending on the topic, issue, or subject.
I find though, that what you think is "nonsense" is in itself up for conversation. I found your examples interesting; homeopathy and psychics unsupported ass well. My belief is through experience and research. However I do agree with the snarky-ass label people put out when I'm not open-minded as they think I should be. But it is continued discourse that keeps the old brain rocking and rolling

That's silly. It's obviously everybody who agrees with me!

I am open minded. It means that I have an open mind about the things that I have decided at this point in time to be open about. Earlier in my life I might not have been this way on some subjects and I might evolve more also in the future. So much for being open minded.

That's like saying, "I believe in freedom of speech, but not for people who spout the type of nonsense that you spout."

There is at least some evidence in favor of homeopathy:

[ncbi.nlm.nih.gov]

Given the exorbitant cost of medical care in the US I expect many people have no option but to treat themselves with some sort of folk medicine or homeopathic method they read about on line.

There is a great deal of evidence for psychic phenomena and some very intelligent people have been open minded about the psychic. Werner Von Braun is one example. The spirit of science is to leap in greedily with an open mind and try to learn about new phenomena. Sitting back and debunking things that don’t fit your world view—that is UNscientific.

I don’t know much about alien visits but I remain open minded.

That leaves god, which is a totally different category. I knew a guy once who ardently attacked at any mention of psychic phenomena, UFO’s, cold fusion, homeopathy, or several other ideas he thought were unscientific. I asked him why he had such strong feelings in that regard. He said that that to believe such things would open the door to a belief in God, and that he could not allow himself to have a belief in God. I interpreted that to mean that he had been scared out his wits by church dogma as a child.

Very unfortunate.

Take the label away. Hmm.