Why is Judaism comprised of so many precise stringencies in comparison to other religions?
Why is conversion to Judaism so strict and difficult?
An intriguing question, but I think you need to split this question into multiple questions. So I'm just going to focus on the first part of the question.
"Why is Judaism comprised of so many precise stringencies in comparison to other religions?"
I can not provide any sources for my answer, because I believe it is a "new answer", however it is one that resonates with me, and I hope will resonate with others.
When a person wants to build a bridge, there are different ways of doing it. In the old days, one might find a tree, cut it down, throw it across the chasm, and hope and pray that the tree is big enough and strong enough to get the people across. As people learned more about bridges and gravity, people started to learn formulas that would predict if a bridge would be strong enough or not. Sometimes, people would make mistakes, and a very large bridge would be built, and then fall to the ground when a wind came. Today, we have many many details about how to build a bridge, and our bridges last longer than they did in the past and they are larger. However they are also harder to build, and the slightest error will get the project canceled.
GD created the world, and He created the rules that allow bridges to be built, in which there can be no deviation. Rav Solevetchik called this the halachot of Din, and strict justice. This is how Gd decided to build his world, where the smallest detail can cause a large bridge to come tumbling down.
So too, Gd gave us laws and halachot in Rachamim, and Mercy. These are laws that can be followed or not followed based on a person's free will. These are the halachot of the Jewish religion, all the laws and minor details, from which the world is built.
Many other people wish to worship Gd in the way that the old bridge builders would worship Gd. They throw some general idea out to the world, and hope and pray that it will lead them on a good path and towards a good life. However they get consumed by this one idea, or 10 or 13, or 5, however many a person can hold in their mind at once, and when a Strong wind comes, their "bridge" gets knocked down, and bad things grow and fester in society. This problem can happen to Jewish people as well, when we try to take the "easy route" or don't pay attention to all the details of how each law affects the other. When we forget that every stringency is a leniency in another issue.
This is why we have so many laws and mitzvot with so many details, so that we can build proper Bridges to Gd.
As for anti-semitism.. It's a completely different question, But just read this section of the Torah.
Torah-true Judaism is neither easy nor difficult to adhere to. It is not chamur, but machmir; it is not kal, but meikel. Meaning that one must not be more stringent than the halakha requires, nor more lenient than the halakha mandates. This is because Hashem wants us to build absolute self-control like Abraham (R. Ammi b. Abba - Nedarim 32b).
Are you asking why Judaism has so much legal stringency compared to other religions? If so, I think your impression of "orthodox" Islam is mistaken. As for the other, that whole "breaking away from the law" thing was largely the point...
Conversion is a separate question, but it is precisely because of Judaism's many laws that it is not taken lightly, but considered as a serious and permanent undertaking.
As it is in its entirety G-d's revealed Truth, it is not in need of justification.