Modern-day atheism is strange. Rather than "there is no evidence other than these religious texts, so I'll choose to believe religions are false," they go with "science shows no evidence of the supernatural, so I'll choose to believe religions are false." Let's say there are 3 people that visit a museum. One display is a large cube with a plaque in front of it. The plaque reads "There is a sphere of gold inside this cube." No method exists in this universe to know if there is anything at all in the cube. One person chooses to believe the plaque is true, one person chooses to believe the plaque is not true, and the last performs every test imaginable in his universe on the cube, and when none of them work, he bases his belief on the plaque's truthfulness on the fact that the tests showed no evidence. It doesn't really matter which position he takes, the point is, he is basing his decision on science when it can not reveal the answer.
Interesting analogy, but why don't we examine it a bit:
1)Reality knows there is no method to know the answer but the 3 people are significantly less informed.
2)Both the first and second individuals formed their beliefs in a way completely causal independent of the answer to the question.
3)A test can be a verification test, a falsification test, or both (technically or neither but we exclude those out of common sense). Likewise tests can be of various degrees of confidence.
4)For there to be no method to know the answer and for there to be methods that person 3 uses to attempt we get some information not previously evident. Namely we know that there are valid methods for related cases (remember person 3 does not know that no valid method exists for this case).
5)It is possible, depening on what you apply your analogy to, that person 3 does not know this case is different from related cases for which there are valid tests.
Person 3, not knowing the significant difference between this case and the related cases, applies tests applicable to the related cases and compiles various false positives and false negatives each associated with the degrees of confidence those tests have when applied to the related cases. At worst this leads to a conclusion that is completely causally independent of the answer (same as the other 2 people). At best it leads to a conclusion that is causally linked to the answer but with unknown correlation (aka the conclusion is caused by the answer but we don't know if it is correct or incorrect). So it is no worse than the conclusions the first and second person reached and could be negligibly better.
Now you are also wondering about modern day atheists.
1)
It is not an inherent condition of atheism to reach atheism via applying the scientific standards towards theology
&& Atheism is not an inherent condition of applying the scientific standards towards theology .
These are independent characteristics.
2)
If I have a strain of bacteria it may or may not have antibiotic resistance. I could test a culture of that strain for the antibiotic resistance by exposing the culture to the antibiotic. If they die off then they do not have antibiotic resistance. However if they survive they could have had the resistance or the bacteria might have just lucked out that time (the bacteria on the culture mutating the resistance after being plated for example). However if they survive there is a greater probability it was from having the resistance than from being lucky.
Notice how in the case of the bacteria surviving I drew a conclusion based upon the test "lack of evidence"(lack of change is more accurate). I mention this just in case it was new information for you (your language did not make it clear). If it is not new information then it is irrelevant.
3)
No, I disagree. The majority of modern atheism is just like person 2. Most of them already lacked a belief. However modern humans are more likely to hold higher standards before flipping their positions(regardless of initial position). In the case of certain claims (a god who could but does not prove their existence but demands belief) it becomes quite obvious in hindsight why the positions don't change without evidence.
I think the difference is that one group bases their beliefs on the need for evidence via something that has nothing to do with theology, and the other bases their beliefs on how they feel.
Getting ideas across effectively is not my strength, so you'll have to work with me here. In my mind, there is no evidence outside religious texts, so I can't really answer your question.
If Jane says she bases her beliefs on the need for evidence via how she feels, isn't that also basing her beliefs on the need for evidence via something that has nothing to do with theology?