The Bible does not address the topic of birth control. Birth control techniques on the ancient world were primarily through abortion–either by the taking of poisonous herbs in non-fatal dosages, or by surgical killing of the children. Also, unwanted children were occasionally “exposed,” which means left out to die. It was a brutal time and the kinds of birth control we have available were not available at all. This will explain why the topic is not covered in the Bible. There is one passage which the Roman Catholic Church has tried to use as a proof-text to supposedly show that birth control is sinful. It is Genesis 38:9 where Onan “spilled his seed” (in other words he withdrew before ejaculation, one of the few methods of birth control available in the ancient world). Onan’s actions are called “wicked” in Genesis, but this is almost certainly because of his gross selfishness, not because of his birth control practice. The reason he was having sexual relationship with his dead brother’s wife is that the Mosaic covenant prescribed this for the purpose of widows being able to have descendants. It was out of a kind of compassion that this was done among the Jews. But this very selfish man wanted to have sex with the woman, but not produce offspring. What a jerk! This is not a passage against birth control but against taking sexual advantage of a woman for blatantly selfish sexual gratification.
So, the Bible does not address the topic of birth control. We are therefore left to apply passages about related topics and biblical principles to address the topic of birth control. For this reason, there will not be consensus among faithful, biblically well-informed believers.
My personal experience is that the great majority of Christians do not consider the use of condoms to prevent pregnancy (and disease in certain cases as well, by the way) to be sinful. Certain kinds of birth control, such as abortion, the so-called “abortion pill” and the “morning-after pill” which end the life of an unborn child is rejected by all, or at least nearly all Christians as sinful and not submitting to God. But, few believe the use of condoms or the pill is sinful. There are exceptions, but they are a majority, and I believe I ought to respect those who have this conviction, even if I do not.
Of course, the main exception is the Roman Catholic Church, but some other very conservative groups agree with Catholics on this. Therefore, those who criticize Christianity because they reject the use of condoms are not criticizing the Bible or Christianity. They are criticizing a rather small portion of those who call themselves Christians–mainly Roman Catholics. (by the way, a significant majority of American Catholics do not accept the teaching from Rome on this and use contraceptives, including condoms).
For these reasons, I have no comment about people who criticize people in a group I have nothing to do with. Person X can criticize person Y, when I am person Z, and I say that is between person X and person Y. It is not my business. If I were asked, I would agree with the one who says that Roman Catholics are dubious for taking this stand. In a world with an ever-growing population, if some form of birth control is not used, then within a generation or so, the population will vastly outstrip the resources of our planet. It is irresponsible for people to have very large families in the present situation. I say this as a human, not as a Christian, as the Bible does not address this topic. I say this as an ethical rather than moral stand. It is based on a situation which did not exist 2000 years ago, which is overpopulation of the earth. Personally, I see no biblical reason to not use methods to avoid having children that we do not want. Sex between a husband and a wife is a beautiful thing, with its almost mystical intimacy, and God created sex, not just for procreation, but to bring unity between a man and a woman. In the current situation, for a man and a woman to engage in this beautiful God-supported activity in a way which does not produce too many unwanted children, and which also does not kill unborn children is a good idea, in my opinion. So, I guess I agree with this proposed person in your question. However, their “beef” is not with Christianity or with the Bible, but with a small subsection of Christians who obey the pope.