"it should not matter"

The notion that these conversations are free is an idea held by a very small group. Most people have reasonable reasons for assuming that the conversation has a cost and therefore you have a motivation for proposing a particular point of view. Some people find conversations emotionally draining, some people perceive every conversation as a risk to one's political capital, other people feel that any time invested in a conversation is a cost that should be recouped at other points, other people are keenly aware of the meta message sent by one's words and therefore the impact on the relationship of those who participate in the conversation. Therefore it is reasonable to assume that most people will assume that a person advancing a viewpoint also believes in that viewpoint, and since that perception is wide spread, if you refuse to acknowledge it with a comment such as "for the sake of argument" then ask yourself why you feel those 5 words cost you more than the 500 or 5,000 other words that you'd like to invest in the conversation.

The point being made is if it's a substantive point it doesn't matter how much the speaker identifies with it, the valid point has been made to you and it is to be considered. Hence it should not matter provided you are sticking to the facts. It seems you have made this into a personal insult about whether or not your transactional view of the costs of speaking are being respected. That is to shoot the messenger.

The person is doing you a favor by pointing out valid concerns even if they don't agree with them.

But if the discussion actually influence real-world decisions then it matters a great deal what people actually believe.

I really don't understand why more people are not getting this.

It can be plenty consequential in the real world, I said from the start of this thread that someone could be arguing a popular opinion that nobody in the room happens to hold.

This happens all the time in silicon valley as an example: a bunch of educated, comparatively wealthy, mostly white men make decisions. Maybe they are not very in touch with the opinions of the vast majority of humans who fall outside that category. What I am advocating for this case is the ability to have empathy for those who are unlike you, step outside your biases and adopt an argument that is not your own. This is a good skill. People are falling over themselves trying to call that lying and universally bad or nearly so.

With parenting - I see no issues. And I do use such an approach, but my spouse, I believe, trusts me.

So... It looks like the problem is - when the debate is used to judge world view of the person to decide if one would like to trust them - such "devil advocate" arguments are harmful. I believe it is just one possible use of the discussion, but I will keep in mind that and try to avoid arguing from some other perspective if I see the person is trying to figure out if they want to trust me or not.