Will Brexit affect British Air Heathrow as a hub to other destinations in Europe? Passport control at LHR and then again at final destination outside of Great Britain? Our next European travel scheduled for 2020.

That's already the case as the UK is not in the Schengen zone (UK and Ireland are in their own, and will still be after Brexit).

The only possible change after Brexit is since EU citizens will have to join the queue for 'Other Passports' like US citizens, Canadians, Australians, Japanese etc, there may be further delay in immigration for entering UK. Also as UK citizens will then have to join the same queue as non-EU citizens in EU countries, there may be delay in entering France, Spain, Italy etc.

I think that OP will just be connecting in Heathrow to somewhere else in Europe.
If so, there will be no "immigration" or passport control in Heathrow - you'll stay airside and just go through security and then to the gate for your connecting flight.
You'll clear passport control/ immigration at your final destination in Europe.

In that case UK citizens, who mostly account for passengers on flights from Heathrow, will be all in 'Other Passport' queue causing congestion and delay as OP goes through passport control at their destination.

I wouldn't expect any relevant delays except for typical holiday destinations like Majorca or Tenerife.
International airports like Paris, Rome or Munich have hundreds of flights from places outside the Schengen area or the EU so that the few extra tourists or business travellers from the UK in the "other" line will probably not cause any relevant disruptions.

Going around various European airports this year and chatting to staff and seeing new signs being prepared I suspect each airport will decide on actions differently. So Geneva will probably go EU/Swiss/UK in one queue for example. Since most areas that handle this are super-flexible, moving the UK about is not really that hard. I doubt very much you will see anything change apart from a few signs.

airports can move around personnel as they need, there isn't any given that this will cause "congestion and delay", if they need more people in the 'other" line, they can move more personnel there, that's all. I presume when this all happened, they moved more personnel to one EU line, whereas it used to just be UK versus everyone else (at LHR)> Why do people not think the management at the airport can figure out where they need people.

Christina, it wouldn't be the airport management, it would be the immigration authorities, who aren't exactly in the business of user-friendliness, nor noted for their common-sense.

Patrick, I think you are being a little unfair to the authorities, no one wants massive queues. Immigration officers have familes too.