No, there is no such word. The closest would be "home training" or "home trainer" but I don't think it is extremely common and is likely to get confused with skill training at home or someone who comes to your home to train you in something.
Moralist reproduces the good denotation of gutmensch with a similar dark connotation:
noun
1.0 A person who teaches or promotes morality.
1.1 A person given to moralizing.
ODO
Almost everyone considers their own morality to be good. Most consider their moral judgments to be superior, or at least on par with the best, but in the modern mind, a moralist is often portrayed with an irrational moral opinion used unsympathetically to cajole and coerce others into conformity against their will.
John Dewey: An Intellectual Portrait, by Sidney Hook, reveals the positive denotation of one who constructs a superior moral framework:
To those who know him by his less technical writings, John Dewey
appears as a great moralist and educator.
In his introduction of The Unity of Plutarch's Work, Anastasios Nikolaidis used moralist with the dark connotations of irrationality and coercion:
These findings, however, do not entail that Plutarch was a crude
moralist who stigmatized deeds and conducts, meted out prescriptions
for correct ways of living or put forward ideal, and therefore
unattainable, patterns of behaviour.
Although the preacher from Nathaniel Hawthorne's The Scarlet Letter was predominantly a hypocrite, he was primarily a moralist, who struggled against his own gutmenschlich qualities at the expense of his secret mistress, Hester Prynne:
The days of the far-off future would toil onward, still with the same burden for her to take up, and bear along with her, but never to fling down; for the accumulating days, and added years, would pile up their misery upon the heap of shame. Throughout them all, giving up her individuality, she would become the
general symbol at which the preacher and moralist might point, and in
which they might vivify and embody their images of women's frailty and
sinful passion. Thus the young and pure would be taught to look at her, with the scarlet letter flaming on her breast—at her, the child of honourable parents—at her, the mother of a babe that would hereafter be a woman—at her, who had once been innocent—as the figure, the body, the reality of sin. And over her grave, the infamy that she must carry thither would be her only monument.
Emphasis added
Best Answer
Uninhibited
Unreserved will also fit quite well.
However, take into account that the level of restraint expected from a guest is strongly dependent on culture. What may you perceive as an uninhibited behaviour, someone from a different culture may perceive as a completely normal one. E.g. if I am invited and my host expects me to reject what he is offering me, I may be quite reluctant to accept his invitation the next time.
So be careful in assigning these words to someone's behaviour too easily.