The answer to this is an emphatic 'yes'. Not only was the position respected but it was one of the most respectable positions that you could have at the time! Of course, nowadays, there's a tendency to view it as a gross, gruelling task (for those who don't know, the position essentially put its holder in charge of the king's 'toilet') - but that fails to consider the dynamics of court politics at the time.

Even though the position existed in some form under Henry VI, it was really established under Henry VII. He wanted to take advantage of the King's Chamber, as opposed to the Exchequer, when it came to managing his finances (something which had really begun under Edward IV). Grooms of the Stool often held significant power, or went on to become very powerful. Hugh Denys, one of Henry VII's Grooms of the Stool, held significant sway over his finances in the last decade of his reign.^([1]) The people appointed also tended to be what Steven Gunn calls 'New Men'. Certainly not peasants but also not members of the traditional nobility, they ranged from the children of yeomen to children of members of the gentry.^([2])

They weren't universally respected by members of the nobility, unsurprisingly, but even those who did not approve of this new class of up-and-comers had to respect that they were holding increasing influence over the monarch (and by extension national politics). The fact is that, as menial as it may seem now, a position like the Groom of the Stool (which necessitated a very intimate relationship) forced the King to appoint people he thought he could trust and then allowed that person pretty much unparalleled access to the King's ear.

What should also be made clear is that the Groom of the Stool was never just supposed to help the King with his... relief but was also one which involved things like distributing the king's alms and travelling with the king.^([3]) This is evidenced by the notable figures who held the position. Hugh Denys (who I already mentioned), Sir William Compton (one of Henry VIII's most prominent courtiers), and Sir Anthony Denny - who was perhaps Henry VIII's closest friend and ally at the end of his life, whose position also had ramifications for Edward VI's regency council.^([4])

What I hope is clear is that the position would have been understood to be a very respectable one. Any position which required an intimate relationship with a monarch would be. The people who respected it the least were members of the traditional nobility who were appalled to see the rise of influential 'New Men', but even that 'disrespect' emerged from a recognition of its significance.

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[1] Steven Gunn, 'The Structures of Politics in Early Tudor England', Transactions of the Royal Historical Society, Vol. 5 (1995), 59-90.

[2] Steven Gunn, Henry VII's New Men and the Making of Tudor England (Oxford: Oxford University Press, 2016).

[3] G. W. Bernard, 'The Rise of Sir William Compton, Early Tudor Courtier', The English Historical Review, 96:381 (1981), 754-777.

[4] Patricia C. Swensen, 'Patronage from the Privy Chamber: Sir Anthony Denny and Religious Reform', Journal of British Studies, 27:1 (1998), 25-44.