I’ve always hated “religion” as a branding. It feels as though it was meticulously created by the Devil to invalidate Christianity. Now, with “religion” as an “established” culture existing, when one goes to spread the gospel of the Lord Jesus Christ, one can dismiss His word as being “just one of many”, or, as the OP’s friend said “all the same”.
One could argue that the branding “religion” isn’t problematic as much as “false” religions are (with Christianity being called the One True Religion), but the title nonetheless affects Christianity’s image when the Word of God has to share its branding with concepts like Jediism (No, I didn’t misspell Judaism; a fictional order from Star Wars has it’s own religion, too).
Unfortunately, this will be a rather troublesome situation to change; arguing Christianity as the One True Religion is nigh-fruitless, yet calling it anything other than a religion may yield more confusion than conviction.
Ultimately, this is a matter for the Holy Spirit; pray for your friend that they may be convicted and saved, and have faith that your prayers are answered.
Edit: The last thing you want to do is alienate them though; recognize them for what they are (and accommodate your relationship around such), but show them Christs’ love in spite of their seeming rejection. Let your life be your testimony; of both the Holy Spirit’s charity, and Christ’s existence.