The answer, I feel, can mostly be summed up by:
Since when is being religious and being focused on God a contradiction? What is being religious? Let's make it official and throw in some Merriam-Webster.
- relating to or manifesting faithful devotion to an acknowledged ultimate reality or deity <a religious person>
- of, relating to, or devoted to religious beliefs or observances <joined a religious order>
- scrupulously and conscientiously faithful
- fervent, zealous
What exactly is wrong with these definitions? In your "personal relationship with Jesus," do you not have faithful devotion toward Him? Do you not hold beliefs about Him and about faith? Do you not stick to those beliefs thoughtfully and fervently? Religion is concerned with the spiritual and supernatural, not opposed to it.
And in the other boxing ring (rules vs relationship), do you not follow rules yourself, like "You must believe in God the Father, the Son and the Holy Spirit and profess Jesus Christ as Lord, who suffered, died and rose again for the salvation of the world."? Or isn't "You should have a personal relationship with Jesus Christ" a rule as well? Attesting to certain beliefs and being guided by a framework does not ruin your relationship with God. Guidelines should strengthen our faith because we become one united Church and because we are forced to evaluate our faith. Why do I want to have a relationship with someone if I disagree with the truth He has laid out?
I do not see why the two cannot go together. Religion has nothing if it does not address spiritual and supernatural subjects. We do use "religious" to describe someone's behavior about things which are not spiritual or supernatural, however. "He watches soccer religiously," for example. But what does this mean? In one way, it refers to the intense, fervent way in which one should encounter and approach faith. He is passionate about and devoted to soccer like one is passionate about and devoted to God. In another way, it refers to the obsessive behavior one acquires. Unhealthy for non-faith matters, but shouldn't we have a bit of obsession when it comes to God?
What does one have instead when they possess spirituality without religiosity? How is a spiritual life oriented toward God without a guide? Is one sporadically tapped into God's grace without action? Is it problematic that "spiritual" may not even necessitate "God?"
Rules guide one's relationship with God. It is natural to have and obey rules. When we were children, our mothers told us to stay away from the stove and to clean up our toys. We likely protested by touching the stove or scattering our toys about even more (I certainly did), but these rules have good purpose. They tell us the best way to live our lives (not burning our hands and not stepping on a Lego, which everyone knows is the worst pain that can be experienced this side of eternity), and even if the rules do not make sense at first because our immature selves have selfish desires, they are ultimately put in place to make our lives better and more enjoyable.
I saw this video months ago and have read several posts and comments since then which all end up sounding like an attack against the Catholic Church more than anything else. I take this view because the Catholic Church has been the longest standing church with unchanged "rules and regulations." There are, instead, enough several thousands other churches which make finding one you can agree with, which won't tack on new rules, much easier than trying to change the Catholic Church. And really, this leads to one of the major problems I still would like to resolve in my attempt to better understand Catholic-other faith relations, and that is greatly summarized by the Venerable Archbishop Fulton Sheen: