I speak only for myself here. Although I do have some Landmark tendencies, I have not bought the whole package. It's evident by my posts, that I'm strong on the local church. I believe that Baptists historically have held to doctrines and practices held by New Testament believers. I believe that that Jesus established his church during his earthly ministry, and that it has continued to exist to this day, although not necessarily known as Baptist.
I won't fall out over the succession issue.
I'm a closed communionist, but it's not a test of fellowship.
And Landmarkism, in any variation, is not a litmus test for a true New Testament church, in my view. I hold that legitimate New Testament churches may disagree with each other on this question. The fact that they are wrong does not diminish my willingness to fellowship with them. If it were otherwise most of the people in my church would have nothing to do with me.
Oh, I forgot to answer your question. A significant number of Southern Baptists are Landmarkers. At one time in its history, the SBC was predominantly ecclesiologically Landmark, although no more.
There are Baptist groups which are full-fledged Landmark, and have formed separate denominations. How they feel about non-Landmark churches, I don't know.