I don't have a problem with religion. I'm a Christian.
Now, there are people who say "I'm not religious, I have a relationship with Jesus." Well, I have a relationship with Jesus too, I did not earn it (Ephesians 2:8-9) but that doesn't preclude me from being religious. The "not religious, but a relationship" claim, in order to work, must rely on a definition of "religion" that is ugly, and if that really is what "religion" is, then I reject it too.
But that's not what the New Testament authors understood religion to be (James 1:26-27, 1 Timothy 5:4), nor is it what society at large understands religion to be. I see the "not religious, but a relationship" claim to be well-intentioned marketing that falls short. Unbelievers who do take that bait will inevitably be confronted with the reality that to live as a Christian pleasing to God, they will need to go to church and worship and pray and obey the commands of Scripture and the Biblical teachings of the church. To some, the "not religious, but a relationship" claim is seen as disingenuous, or more widely, it is not taken seriously.
When we look at a relationship, there will be at least three elements - love (of the appropriate sort), communication, and trust. My relationship with Jesus involves prayer (communication), faith (trust), and obedience (God's love language, John 14:15, John 14:23). Yet, no one can really say these are not also religious. My religion is relational, and my relationship with Jesus is religious.