Not all religions make such truth claims.
Dharmic 'religions', for example, don't have The Problem Of Evil that you mention, even though they address it.
https://slife.org/problem-of-evil-in-hinduism/
Part of the reason for this is that they aren't REALLY "religions" in the strict sense. Colonizers came and made assumptions about their practices and then defined religion in such a way as to deny the vast majority of their radically inclusive outlook and way of life into merely being a religion when they are SO much bigger and therefore more unified than this.
Advaita Vedanta, for example, addresses this problem thusly:
https://www.vedanta.com/store/problem_of_evil_Prabhavananda.php
I say this knowing that SOME of the people who participate in Dharmic approaches to life DO conduct themselves "religiously" in the limited Western conception of what a religion is.
The Problem Of Evil you are mentioning exists because Western religious conceptions are fundamentally dualistic, so their foundational premises are flawed from the outset.
Or, at least, have been made to seem so by the people who have been teaching them. A LOT of what is taught about Abrahamic religions is a corruption of the teachings.
From a dharmic practitioner's standpoint, texts like The Bible read VERY different than what is typically taught in Christian circles. For example, The Sermon On The Mount: https://archive.org/details/sermononmountacc00prab/mode/2up
The fundamentally dualistic and rigid revisionism of our cultural outlook is IMPOSED upon ALL perspectives and then taught in this fashion as though it is perfectly right, acceptable, normal, and even preferred.
Further, any other more inclusive outlook is strictly and often violently excluded and suppressed, even as the people whose perspectives reveal a deeper insight into the nature of reality (what religion is about) are excluded, colonized, and genocided into irrelevance.
What is left remaining (and taught) LOOKS like "hundreds of religions that claim" when in fact this is perhaps the biggest lie ever told.
This results in your question, which has the same flaws in its premise as the culture desires. You are easily controlled, even in a religious context, if you make these fundamental mistakes, and if you make it seems like "all religions are the same, they are all making truth claims".
Even atheists make this mistake, which is hilarious to me.
It's funny because all of the misinformation and disinformation of the Internet age and we all often fail to see the misinformation and disinformation about foundational premises of our spiritual insights that have been distorted and twisted thousands of years before the Internet.
Even reducing spiritual ideas into a book is along the lines of this same reductionist impulse that gradually erodes our understanding as I've outlined here. By having a severe bias against oral or other traditions, you artificially restrict the understanding of religion and the larger ways of life mere religion cannot fathom.
Even English AS A LANGUAGE misrepresents many spiritual aspects since the very definitions of words can only be said to be so from a colonizer's perspective. Authentic religion is far greater than its defined terminology. English is a TERRIBLE language for speaking about spiritual or religious topics in any case, as it's primarily a language of merchants.
Using English to talk about spiritual topics is like trying to use 2-dimensional media to represent a 3-dimensional or 11-dimensional experience. YOU LOSE A LOT.
Some Christians have found solace in adopting the Hindu concept of God as the Indwelling Spirit in all beings. This spirit or Soul (called Atma by the Hindus) is separate from the body and mind and is the same in all beings. It is that of part of you (and everyone else) that is eternal, pure, and is the source of all power/love/happiness, etc. The Soul (i.e. God) is the same in all beings, i.e, we are all His children. Every being searches for happiness in the external world. After getting fed up with the external search, they turn inward to discover happiness within their own heart, culminating in the direct experience of God or Atma. The purpose of life is to realize your own Self (i.e., God).
The above concept of God is not tied to any religion. The Hindus then designed specific rituals to turn the mind inwards towards God as God can be seen only with the pure mind. However, nothing prevents a Christian or a member of any religion to adopt the above concept of God and pray to the God that dwells within all beings. You "love your neighbor" because of the presence of God in his heart.
Christianity has been interpreted and explained with the above concept of God by many people. One such book is https://www.amazon.com/Sermon-Mount-According-Vedanta/dp/0874810507 There is PDF copy of the book floating around the Internet.
Not sure if this addresses your problem but thought I would mention it anyway. Turn religion into spirituality by seeking direct experience of God within your own heart and then in other beings. That might make it more interesting.
>all religions are an effort for man to earn God's favor.
I would say that all religions are an effort for man to reach God, not all religions believe that God's favor can be earned.
>Christianity stands alone in that God's favor is a free gift for all who beleive in Him.
God's favor is not a free gift for all who believe in him. People forget that the other half the requirements. Believe in me (Jesus) and do good works.
The path to a God in these eastern religion is just as free as Christianity. Many eastern religions preach that God's favor (or rather God) is already inside of us, and so does the bible
"Behold the kingdom of God is within you" luke 17:21
Although I consider myself a Christian, I believe that all religions are connected and share the same truths. If you are ever interested in looking in to this theory, I would highly recommend this book. Sermon on the Mount According to Vedanta