Surely the question whether pentagons are more like hexagons than circles just invites the riposte: "more like in what respect?".

If we are interested in whether figures have straight sides and vertices or lack them, then of course pentagons will get put in the same bucket as hexagons, while circles will go in another bucket (with e.g. elipses and parabolas). It's an objective fact that pentagons are like hexagons (and not circles) in having straight sides and vertices.

If we interested in whether we can tile a plane with (regular) figures of a certain kind, then pentagons will be classed with circles (no, you can't tile a plane with those), and hexagons will belong in the other bucket along with e.g. squares and triangles. It's an objective fact that pentagons are like circles (and not hexagons) in that you can't tile a plane with them.

So we might say that the bald question "are pentagons more like hexagons than circles?" is incomplete. It needs to filled out (either explicitly or by context) with some indication of the resemblance-respects which we care about when we ask. But once those indications have been provided, it can (as our examples show) be a straightforwardly objective matter what the answer is.

Similarly, the question "are the paintings of Monet more like those of Renoir than those of Picasso?" again invites the reply "like in what respect(s)?". Where they were painted? Average market value? Average size? Well, it's perfectly objective what the right answer is, if it turns out that it's resemblance in one of those respects which is question. But of course, we might very well be more interested in some more purely aesthetic features; and you might suppose that now things do indeed become more subjective. But the issues don't become more subjective because they are issues about resemblances but because they are issues about the aesthetic. (Another possibility is that the questioner just isn't clear what kinds of resemblance are being asked about: but then we don't have a determinate question to answer.)

In sum: at least some questions about resemblances -- once it is made clear what resemblances are in question -- can have just as objective answers as other questions about a thing's properties. There isn't anything instrinsically subjective about issues of resemblance per se: it depends what kind of resemblances you are interested in.