Significance of the center-tapped transformers in mixer circuits
By mixing low level currents of RF (uV) and LO levels to permit the exponential current of the diodes will create lots of distortion. It is found that the Intermediate Frequency (IF) products of LO-RF and LO+RF are their harmonics are quite useful.
If one chooses the lower difference frequency then chooses carefully designed specs for a low pass or bandpass with bandstops for the higher LO and product sum (LO+RF) , one can get a high-quality frequency mixer.
To demonstrate this I randomly chose RF= 200 MHz and LO = 300 MHz to produce an IF out = 100 MHz.  For the filter I chose an unloaded Chebychev LPF with resonant notches at 200,300 MHz
Typical metrics for conversion efficiency are the ratio of amplitudes for IF/RF and LO suppression as well as dynamic range and noise threshold.