It does not have to be unity gain stable, only if you want to use it so.
There is nothing wrong with achieving stability at a higher gain either.
Since this is intended to be a balanced receiver there is no reason for it to be stable at any gain and have a 60MHz gain bandwidth. It just has to work well at one specific gain. This makes things a lot simpler.
There are a few techniques that can stabilize an opamp. Deane Jensen wrote a good paper on it way back.
1. Reducing the gain in the input pair by adding emitter resistors. Usually small values like 30 ohms work fine, sometimes more is needed. A nice side effect of this is the reduction of distortion in the input stage below the noise floor.
2. Reduce the gain in the input pair by lowering the tail current. Here it would be using a larger R1. A drawback to this is that the slew rate will be less as this current is split and used to charge C1. The slew rate is roughly the Ic on the first CMKT5088 divided by C1 in pF. If Ic is 1mA then it would be 1000/10=100V/uS. Very high slew rates like that spell trouble when coupled with high bandwidth and stability is compromised.
3. Increasing the Miller capacitor, C1 in this case, to increase local feedback. This will also reduce the slew rate of the input. Because now a larger cap needs to be charged. Having a 20V/uS slew rate IS plenty so don't worry about giving up some of it.
4. During my experiments I have found that bypassing the VAS emitter resistor R5 with a small capacitor, 47pF to 100pF, can help with stability and helps HF oscillation immunity. Basically, this increses gain at high frequencies in the VAS as you bypass the emitter degeneration resistor.
5. Using a resistor in series with a capacitor in the feedback network. (Not shown on your drawing). If you think math is too much thinking you can always just use a square wave on your scope and see what values work best. R is usuallt around a 100 ohms and C varies from 15pF to several hundred pF.
6. Adding a small inductor, 3 to 4uH, at the output of the opamp. OK, this is sort of cheating and just cuts the HF crap out and does not really stabilize the opamp, but it is effective at presenting a clean signal to the next stage.
This is not necessary, but I would rather add a current source to the VAS transistor (T1) instead of adding a VAS buffer. When you add a VAS buffer you increase the gain of the VAS to Hfe of 10,000 and beyond. This will give you a stability headache that will be a total PITA to overcome.
Gus is referring to the output clipping asymetrically when you overload it with signal or laod it with a low Z. I think receiver like this would be followed by something that has at least a 10k input impedance so single ended is not that bad. However, you will clip asymetrically when overloaded by a very large signal.
You can increase the CMRR of the input stage by replacing the 12k resistor with a current source. This should give you at least a 20dB improvement in CMRR that is not a bad thing in a balanced line reciever.
In summary the most bang for the buck would be adding current sources to both the input and the VAS, and adding emitter resistors to the input pair. Too bad this circuit is nearly impossible to breadboard due to the CMKT5088 being such a tiny turd. You could do it by using two 2N5088s in the prototype though.