I think your confusion is about the rule that "when components are in parallel, the voltages across them are equal".
Let's look at the simplest parallel circuit:
Resistors R1 and R2 are in parallel.
The reason for the rule is that potential (voltage) is a property of a node in a circuit or a position in space. If we have a charged particle at B, and we move it to A, no matter how we get to A (either by passing through R1 or R2), we will have to add the same amount of energy to get there, defined by the potential difference (voltage) between A and B.
Now let's look at two voltage dividers in parallel:
Now the R1-R3 combination is in parallel with the R2-R4 combination.
If we take a charged particle from B to A, it doesn't matter what path we take, it always requires the same amount of energy.
But that doesn't force any equality between the potentials at X and Y. From an electrical potential point of view, X might be "10% of the way from A to B" and Y might be "90% of the way from A to B".
For example, let's say B is at 0 V, and A is at 100 V. Then if R1 and R3 are both 50 ohms, we know from the voltage divider rule that X is at 50 V. This has no dependence on R2, R4, or the voltage at Y.
If R2 is 30 ohms and R4 is 70 ohms, then the voltage divider rule tells us the voltage at Y is 70 V. Again, it doesn't depend at all on R1, R3, or the voltage at X.
Finally, let me double-check one other thing you might have gotten confused about. Here's your schematic again:
Notice where the two lines meet and I put a red circle, there's a heavy "dot" at the intersection of the two lines. This dot indicates the wires are connected at that intersection.
Notice the other place where two lines meet and I put a blue circle. There's no dot at that intersection. This means the two wires are not connected there. So there's no parallel connection between the upper two resistors. The only parallel connection is between the voltage dividers as a whole (Like my second example, above).