Of course the individual teachings and practices of a particular denomination can be the subject to criticism by other Christians.
For example, I think Calvinism is completely bonkers and that John Calvin strayed very, very far from traditional Christian dogma. I vehemently disagree with all five "TULIP" teachings of Calvinism.
But strongly disagreeing with the theology overall does not mean I would EVER say anyone who is a member of a Calvinist denomination "is not a Christian". It would extremely insulting and divisive to make public comments like "There are Christians and there are Calvinists. These are NOT the same thing. You CANNOT be a Christian and accept Calvinism. The Calvinists are a made man cult that worships John Calvin as their savior, and no Calvinist knows Jesus Christ as lord and savior. They must accept the true Christ of the bible and leave the false religion of Calvinism to be saved."
Now, replace the word Calvinism with Catholicism, and a ton of "evangelical leaders" DO spew that kind of nonsense. You can't "show compassion for fellow brothers and sisters in Christ" if you're not even willing to acknowledge they ARE Christians to begin with. To guys like Ray Comfort and his ilk, millions of people who sincerely believe in the Holy Trinity are no different than Buddhists.
As I noted, I think Calvinism is absolutely wrong. But I would NEVER claim a devout Presbyterian who fervently believes Jesus is fully God and fully man and that God the Father, God the Son, and The Holy Spirit are all different forms of the same loving God is "not a Christian" merely because he's a member of a calvinist church.
I generally agree with your position. In fact, I generally agree about Calvinism. But there are Calvinistic teachers I respect very much. I just don’t agree on some specific teachings, like 5-point Calvinism.
“To guys like Ray Comfort and his ilk, millions of people who sincerely believe in the Holy Trinity are no different than Buddhists.”
I have watched a lot of videos by Ray Comfort and believe that he is not only a true, born-again follower of Christ, but also a very good and gifted Evangelist. I cannot speak for him on his views of Catholicism, but what I’ve seen in his public videos is a willingness to engage anyone with a challenge as to whether they have repented of their sins and trusted in Christ for salvation. This offends a lot of people from all walks of life who tend to think the message proclaiming their need for salvation is offensive. These may be atheists, Catholics, Protestants, or others.
The reality is that people can grow up in a Catholic or Protestant church, or even be a clergyman of such a church, and have never actually received the gift of eternal life.
I’ll go further on your example. The demons know the Trinity is real, but they do not have saving faith. A person who has received a great deal of the truth and has heard the Bible read and proclaimed is in more danger than the Buddhist who never heard the message of salvation, unless they also respond to the message with repentance and faith. To whom much is given, much is required.
When people with a church background hear the Gospel preached to them, often they become defensive and rely on their church membership as evidence that the message is not for them. But it is especially for them (i.e. us). In the rare cases someone tries to share the Gospel with me in public, I let them know I already have trusted in Christ for salvation. I don’t get defensive because I’m glad that someone cares enough to try to win lost souls. If they are preaching a false Gospel though I warn them and give them scripture on what the true Gospel message is.
Believing in the Trinity does not equate to salvation.
Even the demons believe i n God and tremble, but cannot be and are not saved.
So sincerely believing in the Holy Trinity is not what saves someone.
Your polemical recourse to extreme unsubstantiated broad brush assertions (unlike those by popes who do damn all who do not live and die in the bosom of Rome) does not help your argument.