Some Google examples for you:
At non-normal incidence the losses increase and are different for the TE and TM fields [4], but these effects are generally small enough to ignore for the ...
... multi-way covariances are usually small enough to ignore (Dakins 2003). Covariances can be positive or negative. A negative covariance reduces the overall ...
For Lyons, his 1946 contributions are certainly small enough to ignore.
... the target had been 238U; the differences in the barriers and radii are
considered small enough to ignore for the purpose of the following discussion. ...
The religious corollaries are easy enough to ignore and the visual splendor for
a good part of the film will keep you well enough distracted from the ...
Rules that the US and the richest nations are strong enough to ignore when it is
to their benefit. Poor countries on the other hand are ruinously penalized ...

So many slaves on the Internet

OK, there are such examples, but not too many to make it a norm
Btw, Rules that the US and the richest nations are strong enough to ignore when it is to their benefit┘ is a different construction. You cannot possibly say " Rules that the US and the richest nations are strong enough to be ignored┘

In case you don't trust Google, here are some examples from "A Practical English Grammar" (Cornelsen & Oxford University Press), p. 179 "Adjective/adverb + enough + infinitive:
... the infinitive can refer to the object of the verb:
After a few minutes the coffee was cool enough to drink.
The case is light enough (for me) to carry.
... it can refer to the object of a preposition:
The ice was thick enough to walk on.
The light was strong enough to read by.
In my sentence the passive voice is more common which I have admitted already, but it is not impossible or wrong.
Don't get upset, guys, you will find enough mistakes in my postings, but this one is NOT a mistake, sorry

Sorry I haven't delivered 1000 examples to convince you. But even these 5-6 examples prove my sentence to be correct though not the only correct version.
If you change it to read: .... they are big enough for us to ignore them, it will also sound better but it is possible to omit the object in this case as shown in the examples.
Can't we change the topic or are you determined to argue long?

You are right, I agree.
I should have checked more than the first page in Google before making conclusions.
Actually I am glad that the reason your message didn't struck me as incorrect when I read it first was that it was correct (as opposed to slavery)

I am glad you see it this way
Once my American friend said about himself: "I certainly don't always speak correctly, but at least I usually know what's right if I have enough time to think!"
I think that it suits all of us perfectly well.
I often have to argue with my students who fail to see and accept my corrections because they think German and try to speak English. After the fourth or fifth wrong sentence I start to doubt myself and consult the dictionary.
And I can never hark back to Russian - I have to think in two foreign languages at the same time.

Am I completely stupid, or what?
Phrase:
After a few minutes the coffee was cool enough to drink.
brings correct meaning. We divide that phrase to understand better:
After a few minutes the coffee was cool |||| enough to drink.
And your original phrase
they are big enough (for us) to ignore them
has meaning opposit to what you try to bring to us. The meaning, again, can be understood better if we divide the phrase:
they are big |||| enough to ignore them
So your original phrase can be exaggerated like that:
If they would be even bigger, we shel ignore them even esier.
(well, I never pretend that I can use "if" sentence, but hope that my logics is understandable)...

You are not stupid at all but you lack some knowledge of grammar which is normal for a person who has not studied the language at university. Ariet seems to have a good language education and knows a lot about infinitive constructions.
That's why she understands me and you don't
You cannot separate the words "big" and "enough" in this sentence. They belong together like "too big" or "rather big" with the only difference that "enough" should follow the adjective or adverb it belongs to and not precede it. The same is true with cool enough, smart enough, fair enough, etc.
... they are big enough (for us) to ignore them - is an infinitive construction which is typical of English. You can change the phrase to read: they are too big (for us) to ignore them but the meaning will be more intense which I wanted to avoid using "enough". What I wanted to say was that the differences cannot be ignored only because there are a lot of them and they are rather important sometimes.
Ask your Norwegian friends if you don't believe us
And what about the examples from Google? Don't they convince you? They are taken from British and American Web sites.

I have no problems with Google examples. They all understandable. Especially the first:
... small enough to ignore...
Further. Two examples from your last post have completely different meaning:
big enough (for us) to ignore them = достаточно большие, чтобы ими пренебрегать
too big (for us) to ignore them = слишком большие, чтобы ими пренебрегать
Теперь смотрим на первый перевод. Двойное зсначение:
1. если бы они были есче большэ, то пренебрегать ими было бы легче;
2. то значение, что Вы имели в виду.
One of my suggestions, that you criticized above (not small enogh to ignore) does not have that dounle meaning...
To conclude: "big enough to ignore" is vague, imho.

I never criticised this sentence, on the contrary I said that it is another option to express what I mean.

That is exactly what I meant in my first post! достаточно большие, чтобы ими пренебрегать and if you read the message, you'll see it!
Maybe you don't understand the meaning of the word "enough" which is not restrictive (big enough means not too small).
And now change the topic, please. Maybe I am not smart enough to explain it to you, so I resign. If you think that you know it better, then go ahead and discuss it with somebody else.

That discussion is not at all about English, because we both translate that phrase the same way to Russian, but still disagree on the correctness.
Can you correct my phrase from above, please:
If they would be even bigger, we shell ignore them even easier.
I▓m sure it is incorrect.

Is it a kind of test?
You know perfectly well that it is wrong and I am sure you know how to correct it.
Anyway, I'd put it like this:
If they were (even) bigger, we would ignore them more easily.
If they were (even) bigger, we would find it easier to ignore them.
In any case you shoudl use Conditional II here. These are only two options, but there are a lot more.
translate INTO Russian
ignore + adverb (ignore easily)

Thanks. No that was not a test. You see, I work in natural science, and there is no way we use that forms in papers... So, I don't have any experience in that.
I hope I will remember...
About comma in that sentence. Is that comma necessary in all interpretations of English? I mean, are there difference between interpretations in using punctuation?

A comma is necessary only if the If-clause precedes the main clause:
We would ignore them more easily if ...
If they were bigger, we would ...

Why don't you join in a scientific forum of native English speakers? It would be more useful if you communicated with people who are sure in their use of English and you could discuss scientific topics as well. This would improve your knowledge enormously.
Try these: http://www.groupsrv.com/science/forum-14.html
http://magma.tamu.edu/cgi-bin/YaBB.cgi
You can find a lot on the Internet