I would be worried it the Sun didn't behave normally. Transitioning from Dipolar to Quadrupolar back to Dipolar is how it works. It happens when the Sun reaches Solar Max, just like it's doing at present. Here is a thorough paper on it from 2002;
Observations of the Sun’s magnetic field during the recent solar maximum
[link to www.ias.fr]

"We show how this influenced the current sheet. At solar minimum, the Sun’s coronal magnetic field was essentially dipolar and aligned parallel to the spin axis. As a result, the heliospheric current sheet was flat and had very little warp. Around solar maximum, the dipole was perpendicular to the spin axis, and the ratio of quadrupole to dipole strength was high for much of the time. This meant that the current sheet was tilted and highly warped, and reached up to high latitudes. Surprisingly, there were also times close to solar maximum when the quadrupole/dipole ratio was low, and the current sheet was relatively flat, but still highly inclined. We apply for the first time to solar magnetic data a method, which quantitatively analyses the quadrupole component of the magnetic field..."

For those that like videos, there is this;



For those that like to read, here is another paper;
Dipole-Quadrupole dynamics during magnetic field reversals
[link to www.phys.ens.fr]

"In conclusion, we have used a simple method to extract the dipolar (antisymmetric) and quadrupolar (symmetric) components of the magnetic field in the VKS experiment. We have shown that this decomposition allows to investigate the morphology of the magnetic field during reversals, and to compare experimental results to the predictions of a recent model proposed in [11]. We have shown that the results of the VKS experiment are in very good agreement with these predictions:
- reversals are characterized by a strong transfer to the quadrupole when the dipole vanishes,
- the dipolar mode systematically displays an overshoot after each reversal,
- random reversals are asymmetric, i.e. involve two phases: a slow one triggered by turbulent fluctuations followed by a fast one mostly governed by the deterministic dynamics..."

A few others;
A Star with two North Poles - 2003: [link to science.nasa.gov]
The Sun Does a Flip - 2001: [link to science.nasa.gov]
The Sun's Polar Magnetic Field, 1959 Paper discussing the delayed Polar Flip: [link to adsabs.harvard.edu]

Since modern observation began, the Sun's default has been to possess two opposing poles. During polar reversal, while the magnetic fields are in chaos and sorting themselves out, the two poles often have the same polarity temporarily and at weak strengths. Then as the reversal proceeds the poles settle in opposing polarities and power back up to full strength.

That phenomenon where the poles share the same polarity during the transition of a reversal is not noteworthy, it's occurred the last 3 cycles. That is not what the Hinode team is talking about. Unlike in the past, this time what we have is one pole reversing while the other pole does nothing. If trends continue, we will have both poles having the same polarity at full strength and they will just cement themselves that way until the next reversal.

That is what the term 'quadrupole sun' means. Two poles of the same polarity, cemented. This has never occurred since modern observation began. What a quadrupole sun would mean for us is anyone's guess.