I suppose there is hypocrisy in "The Buried Life" because the speaker is addressing his lover, someone with whom he must intimately know, and yet he speaks of some barrier to that intimacy. In the second stanza, the speaker asks:
"Alas! is even love too weak
To unlock the heart, and let it speak?
Are even lovers powerless to reveal
To one another what indeed they feel?
The speaker then goes on to compare the lack of intimacy and lack of depth in communication with his (and others') own inability to understand himself (humanity) on a deeper level. The larger theme is this dichotomy which is not necessarily hypocritical since the speaker is at least trying to tune into his true self as much as he is trying to commune with his beloved in the deepest, most soulful level.
In the 5th stanza, the speaker notes that we look for moments when we might "inquire into the mystery of this heart which beats." And this occurs amidst the noises, distractions and superficiality, presumably of daily life but also of the modern industrial world.
The speaker compares the depth of water with the depth of the soul, both of one's self and of the depth of connection with others. He compares life with the flow of the stream. It is ongoing and this is natural but the speed is comparable to the hustle and bustle of daily life. One interpretation of the poet's wish is that he might slow the stream down in order to peruse its depths just as he wishes to do the same introspectively and with his lover.
In the 6th stanza, he notes these moments of clarity, connection, and introspection are rare. So there is some sense of resolution of this dichotomy of surface realities and deep thinking, understanding, and love; the moments are rare but at least they are possible.
This hypocrisy is more like a dichotomy or more practically speaking, the frustration of someone trying to seriously feel and think deeply despite the noise of the world and in spite of any condemnation by others. This last point is shown in the second stanza, when he says:
I knew the mass of men concealed
Their thoughts, for fear that if revealed
They would by other men be met
With blank indifference, or with blame reproved;
If the argument is hypocritical, it is because the poet (or speaker) knows what the obstacles are. He knows that "fear" of the reprove of others makes men do things not true to their nature. He knows that people let things get in the way of deeper understanding and deeper intimacy. So, if he is hypocritical, it is because he knows these things and yet does not (or chooses not to) overcome them. However, another interpretation is that he chooses to overcome them and is only occasionally successful. If this is the case, then this poem is not about his hypocrisy; rather, it symbolizes his frustration in himself and his attempts to achieve deeper understanding and connection with his lover.