Agreed. In my experience, the giveaway that someone is a Marxist (or Marxian, if you prefer) is that they refer to the status quo system (subsidies, bailouts, anti-competitive regs, licensing requirements, etc.) as laissez faire capitalism, sometimes using the terms “neo-liberalism” or “cultural capitalism”.
Not everybody who talks that way is a Marxist by any means.
First of all, there's a tradition in Christianity of backing away from the idea of extreme laissez-faire or materialism, even when laissez-faire doesn't really exist. It's left over from the past. Any institution that's been around long enough has a lot of baggage, a lot of slogans and pronouncements left over from earlier conflicts. It's also way of shoring up one side of your political foundation and getting on to other matters.
If "laissez-faire" is a bogeyman that people just attack as an unthinking reflex or a zombie idea that no longer corresponds to much in reality, "Marxism" is similar in the way it gets thrown around and applied to people and situations where it doesn't really fit. So you guys may not be as different as you think..
Secondly, some people who come from poor countries or went through the Depression or entered religious vocations do want to maintain some distance from complete celebration of free markets. In itself that doesn't make them Marxists or Communists or socialists. They may be willing to give a cheer or two for capitalism, but don't want to give all three cheers.
Perhaps one influence is the religious impulse to give full assent only to God. We understood all that back in the Cold War, when it was necessary to get people of very different views together in the same boat to oppose actual Communists or Marxists. It would be a pity if we lost that understanding now.