I'm not being diplomatic. It depends on the type of relationship.
I have friends from all sorts of backgrounds.
I've tried romantic/sexual relationships with men from various background, and those
who didn't have at least a similar educational background never lasted very long.
They lasted longer if the sex was good, but sooner or later, people have to get vertical
and have actual conversations. If I can't have even a basic conversation about most topics
with someone, it's not going to last.

Yes, they do. The degree to which they matter depends on the individuals involved.

They shouldn't but they do.

Yes, a older person has for the most part more life experience. There are times when someone older had basically done nothing or a younger person has gone through a lot, but normally that is not true. Looks if you like it or not always come into play, if you are not attracted at all then it's going to be hard to build a relationship. Although I think the more secure a person is with their looks the more attractive they are. I know really ugly (physically by common terms) people who always attract very attractive people. I know a guy that was seriously injured in a fire and always has a pretty girl at his side (he's not rich either). Culture can be one of the hardest to overcome because your actions are a result of it. My brother is Asian adopted and ended up marrying a adopted Asian girl because he could understand the white culture or the Asian culture because he is a part of both. Education is probably the hardest to adjust. I don't mean level of education, but overall intellect. If you can't carry a conversation then the relationship is done. I do think it can work with any of these sometimes it's a little harder. To me communication is key.

For a romantic relationship? Yes. Too young and I can't relate. I need intelligence and at least some kind of education in a partner. If they're from too different of a socioeconomic background, again, I can't relate. And even though I don't have any business having standards when it comes to looks, I can't completely do away with them.

No, unless you're talking about a marital relationship. In the case of marriage, age is a practical consideration, but even that isn't a real stumbling block unless the age difference is extreme. Educational background is not important but intelligence is to a degree in regard to compatibility.

Yes of course. It has been shown over and over with only a few exceptions that people are going to be interested and sexually attracted to soneone they may relate to. Color,age and educational background will not play as big a part as how culturally they are in tune.

Definitely. My ex didn’t value knowledge or education and it became a significant conflict in our way of viewing and interacting with the world. Age probably matters less the older you get, but being in a different stage of life certainly creates complications. Differences in culture can be overcome, but is something you would have to be so aware of, I think it could be exhausting.

I think aspirations and desired lifestyle trump all of those. If you want to change the world a relationship with someone who just wants a quite life isn't likely to work. If one person's world revolves around football and the other is right into the arts or science still likely to be a problem.
And if the great outdoors is your thing the other person has to be fit enough to keep up.

There has to be something in common but age, culture, look and educational background don't really capture those things, though I must admit to having a prejudice against career military men as their outlook seems to be so heirarchical and ordered (I was married to one for 20 years) and I'm more nonconformist.

Not sure is this answers your question, but it has helped me tremendously in building relationships...
[davidpbrown.co.uk]

Nope, I care more about the person's character.

Of those listed, only age strikes me as something that could be a deal breaker.

Yes, all of that; but, most importantly, gender. At least if you're meaning (romantic) partnership type relationship. If you mean any kind of acquaintanceship/friendship, then, those factors would be less important, at least to me.

Friends no. Romantic relationships yes to an extent

Not to me.

Honesty, integrity, humility, kindness, compassion, intelligence--those are the attributes I value. Culture and education may (and usually do, to some degree) influence these, but they don't have to have a controlling share.

If she has that sparkle of humour and intelligence in her eye, then everything else is secondary. It doesn't have to be romantic, just that connection. And if she makes me feel clever and funny - well, then, that's the deal sealed, isn't it?

All of it yes - though it can vary greatly from one person to the next, as each person comes with their own particular "package" of traits, along with strong and weak points.

Age and culture No, because as long as you are alert and interested in others ,no problem. I think educational background is the widest gap to bridge mainly because going through the systems you get so many different 'languages'. I mean that for instance I have never had any sort of background in mathematics or logic etc and couldnt easily connect to someone of that ilk. In the same way there are many many people who come on a person centred counselling training course and never get it ( In my experience teachers are especially unable to disconnect enough from their teaching style in order to get different skills).

Kinda? Someone can be a great conversationalist, but have no chemistry in person. Sure, all that stuff matters, but nothing in stone. It’s just easier if you have anatomy in a similar scale and have similar interests and background. I’ve noticed the same is true for my dog. That being said, a clone of myself would be boring. Being too similar might make it easier to communicate, but it can also be boring. I’m small, wirey and cerebral... I seem to get along best with women that share those qualities... but I’ve had good times with ladies that were a bit taller than me as well. Can’t do the overweight thing though, even if they are smart and otherwise cute, a lot of extra weight is a big turn off... unfortunately a common trait of a lot of smarter folks, in my observation. All that sedentary activity. I guess I prefer those that enjoy physical and mental activity with equal vigor?

They can make a difference in terms of how much common ground you start with, but it is only useful if you are seeking out alignment. It’s not useful when seeking out relationships of diversity. You only learn new things from diversity.

i prefer someone my own age , education but still love meeting anybody up close and personal. just met a couple last night very in love with a 23 year age difference !!!

Culture and age are most important to me. I married a man in his 40s when I was in my 30s. I felt like we had such huge gaps in interests that we just couldn't overcome. He honestly expected me to quit my job and let him support me just so I could be available when he felt the need to do something.

Yes. Of course—I’m human.

All of the above.

I consider all of them but if it feels right and that special something seems to click, you can throw that all out the window