Are the blue and grey 12v train system compatible?

The answer is yes.

Using the 13v~ (alternate) output of the grey line transformer you can command the blue line switches.

This is not in the manual of the new transformer (it is a kind of hidden door to the past) and the blue line transformer switches output was 16v~, but I've tried it and it works.

I just got some blue era stuff. I'm going to try and see what happens, but the grey era Transformer has >13V output and I think that is legacy for the blue track stuff. So that you can plug in switches to there (until now I've wondered what on earth that output is for!!)

It's more or less obvious that tracks themselves are compatible, although blue rails won't go on dark gray sleepers, which isn't really a problem. You may want to use more sleepers under blue tracks to stabilise it, although the 12v inserts help. Mixing blue and grey track and inserts shouldn't be a problem, should you wish to do so.

Motors are also compatible and pick up power the exact same way. Cables use the same connectors and are thus compatible too (if you want to add lighting to your trains).

As for accessories, I can't be sure but I believe there are limitations. If you look at the blue transformer, you'll notice the output to remote control the switch is 16v AC, while grey era remotes use 12v DC. Feeding 12v remotes with 16v might work (it's just an electromagnet inside and shouldn't be exposed for too long), if the blue era remotes need 16v, they may not work with only 12v.

Moreover, the wiring is also different: 12v era remotes use a standard cable, and the polarity determines the direction you want to turn it, but the blue era points use a 3-wire cable, as evidence by this extension cable. And let's not forget the difference AC/DC, which mean you'll have to add some non-LEGO components to make it work.

In short, I think controlling 12v era remotes with the blue transformer should be easy (a couple of diodes should do the trick), but the opposite might prove tricky, and if you have blue points, you may want to get a blue transformer as well. (Then again, I don't know enough about electronics to know how tricky it would be).

A small caveat though: I assumed you have the blue point without the remotes themselves, but since they were sold together, it could be that you get the point, wiring and remote together. If that's so, you best bet is to use the 12v AC output of the 7864 transformer - maybe that's its purpose (and if you try that, and it works, please go answer that question).