Theravada and Nagarjuna I appreciate that various aspects of Nagarjuna's teachings are rejected by Theravadans but I'm wondering where the line is drawn. For some of his teachings I can see room for scepticism, but what about his central argument? Four questions...

In his Fundamental Verses Nagarjuna demonstrates the absurdity of positive or extreme metaphysical positions. 

Do Theravadans accept this proof as valid and sound? 

Do they accept its result, which is the logical absurdity of extreme views? 

If they do accept this logical result, do they also accept the falsity of such views?    

If they do not accept N's argument, on what grounds do they not do so?  

EDIT: Perhaps I should have asked just this. Is it possible to endorse the logical result of Nagarjuna's argument in Fundamental Wisdom and remain a Theravadan?
You are referring to a full book comprising of 27 chapters, with at least ten different translations. That makes it hard to know what the &quot;positive or extreme metaphysical positions&quot; are for someone unfamiliar with his writings, so the question may be difficult to answer without specific references.
Anyway, with all due respect for Nagarjuna, from a fundamentalist approach here are some suggestions for demarcation criterias from the nikayas.
AN 4.77:

Mendicants, these four things are unthinkable. They should not be thought about, and anyone who tries to think about them will go mad or get frustrated. What four?
The scope of the Buddhas …
The scope of one in absorption …
The results of deeds …
Speculation about the world …
These are the four unthinkable things. They should not be thought about, and anyone who tries to think about them will go mad or get frustrated.

https://suttacentral.net/an4.77/en/sujato
MN 63:

These positions that are undeclared, set aside, discarded by the Blessed One — 'The cosmos is eternal,' 'The cosmos is not eternal,' 'The cosmos is finite,' 'The cosmos is infinite,' 'The soul &amp; the body are the same,' 'The soul is one thing and the body another,' 'After death a Tathagata exists,' 'After death a Tathagata does not exist,' 'After death a Tathagata both exists &amp; does not exist,' 'After death a Tathagata neither exists nor does not exist' — I don't approve, I don't accept that the Blessed One has not declared them to me. I'll go ask the Blessed One about this matter. If he declares to me that 'The cosmos is eternal,' that 'The cosmos is not eternal,' that 'The cosmos is finite,' that 'The cosmos is infinite,' that 'The soul &amp; the body are the same,' that 'The soul is one thing and the body another,' that 'After death a Tathagata exists,' that 'After death a Tathagata does not exist,' that 'After death a Tathagata both exists &amp; does not exist,' or that 'After death a Tathagata neither exists nor does not exist,' then I will live the holy life under him. If he does not declare to me that 'The cosmos is eternal,'... or that 'After death a Tathagata neither exists nor does not exist,' then I will renounce the training and return to the lower life.

https://www.accesstoinsight.org/tipitaka/mn/mn.063.than.html
MN 2:

'Did I exist in the past? Did I not exist in the past? Who was I in the past? How was I in the past? In the past, who had been I and who was I [in the subsequent existence]? Will I exist in the future? Will I not exist in the future? Who will I be in the future? How will I be in the future? In the future, having been who, who will I be?'
Also as regards the present, uncertainty arises in him thus: 'Do I exist? Do I not exist? Who am I? How am I? From where has this soul come? Where will this soul go?'
In a person who thus considers improperly there arises one of the six [wrong] views. The view 'I have self' arises in him really and firmly. Or, the view 'I have no self' arises in him really and firmly. Or, the view 'I perceive self through self' arises in him really and firmly. Or, the view 'I perceive non-self through self' arises in him really and firmly. Or, the view 'I perceive self through non-self' arises in him really and firmly. Or, he has the view thus: 'That self of mine speaks, knows and experiences the results of wholesome and unwholesome actions. That self of mine is permanent, stable, durable, incorruptible and will be eternal like all things permanent.'

https://www.accesstoinsight.org/tipitaka/mn/mn.002.bpit.html