No it is not....
If it were a completely private matter then Christ himself would not have taught "publicly"..nor would he have encouraged His followers and appointed Apostles to do likewise.
As Christians we are definitely called to defend the faith as well...especially when up against falsehoods which keep people from the truth Christ would have them to know...
False religions and cults are 'the distraction' to keep people otherwise occupied and away from the true Savior Jesus Christ...they would not be so vast in numbers were it not for the success of accomplishing just that.
We are called to bring down the strongholds which enslave people to false religions...and the teachings which bait them under the disguise of Christianity when they are not that at all...
In the Garden the enemy of men's souls stated.."Has not God said"? and til this day he continues to delude and persuade by using Christina terminology to bait and trap the uniformed of what God "really has said.
So no...Religion is not a private matter at all for it is not about religion...it is about a true relationship with the living God.....and that relationship is seen and read by all men.
how one worships is their OWN business. it is no business of mine, yours or anyone elses. Why do I care how anyone worhips. I worship my own way and respect others who do the same.