If an amp has 4 ohm taps

So I would think that generally speaking, if one had an amp with only 8 ohm taps (which is probably includes quite a few amps) one shouldn’t even consider speakers with 4 ohms listed as nominal impedance.

I’ll let the more knowledgeable and experienced answer most of what your questions are, but regarding this, the manufacturer would know the answer to what the capability of his amp is.

With the Coincident Frankenstein stereo 300B, I noticed it had 8 ohm taps only, so I asked the designer/owner if a 4 ohm speaker is fine, and the answer was that the 8 ohm taps are fine for any speaker from 4 to 12 ohms.

And this is what the manufacturer of my 45 amp states, but he is Japanese so read through the translation:

"An 8-ohm terminal has come out of 1 set of speaker terminal of this machine.
However, the speaker from 4ohms to 16ohms can be used.
Since it will lead to a sound quality fall if a middle terminal is prepared in an output transformer, it is being dared to make the output terminal into 1 set.
Although a little maximum output falls by speakers other than 8 ohms, a sound has little change and it can be satisfactorily used for it."

I can confirm both amps sound fantastic with my 4 ohm speakers; no idea if the tubes will last longer because of the "reduced maximum output" or if other factors are in place. I have heard my speakers are a flat and "easy" 4 ohm load, but I can't confirm. 

FWIW a 'nominal impedance load' of 4 ohms doesn't preclude the load from going lower to say 2 ohms or less at some frequencies which would require a high current amp. Most folks I think stay away from tube amps for just that reason, i.e. they don't drive low impedance loads well. Using the 4 ohm taps doesn't remedy this much if at all. Best to ID your speakers actual impedance 'curve' before you try to match your amp and speakers. Asks the manufacturer (?) or look for reviews which might have identified it.

 they don't drive low impedance loads well. Using the 4 ohm taps doesn't remedy this much if at all.

Thanks @newbee , I guess that was basically my question.

 a 'nominal impedance load' of 4 ohms doesn't preclude the load from going lower

Right.  The 4 ohm speaker I was kind of sort of looking into was the Totem Twin Tower Bison which has a listed sensitivity of 90 dB and the best I've been able to do so far on finding out how low it actually does go has been an AI answer of maybe 2.8 ohms.  

Impedance Curve

The link above is the only impedance curve I can find for those speakers (scroll down).

It looks like it doesn't go much below 3 ohms but it definitely not a flat curve.

My Magnepan LRS+ are 83 dB but have a relatively flat impedance curve around 3 ohms. They sound magical with my Muzishare X7 tube amp on the 4 ohm taps.