The short version: If handled correctly, this is a problem for the avionics suppliers, not for the avionics customers.
"I'm a manufacturer" might be a stretch... Sounds as if I'm sitting at my kitchen table with a soldering iron...
But, yes, my current client is using lead free solder throughout their product line and has done so for a few years now, and there are no problems I'm aware of because of that. Those are not aviation, life support critical or milspec products, but not short lived consumer products either. Reliability and quality requirements are strict.
However, a
lot of effort is required to learn how to do it and make it work. If an existing product has to be upgraded to RoHS compliance it requires a major redesign, including replacing components that will not survive the higher soldering temperatures and altering the board layout. Newly designed products are RoHS compliant from the start. There are major issues with lead free soldering, but those issues can be overcome.
While the company in question learns how to do that, they will probably have problems. If their quality control is good enough it will mostly be yield problems, but if the quality control is lacking substandard products could make it to the customers. The latter is of course the case even if lead free soldering is not used...
However, my point is that it is possible to make products that are just as reliable with lead free solder as with leaded solder. If the supplier knows their stuff, the customer will not even notice the trouble the supplier has to go through to make their products RoHS compliant. Except possibly by a slightly higher price; the supplier needs to recover the significant costs of the upgrade.
Lead free solder is not new anymore; those suppliers who are bound by the RoHS directive have learned how to do it, and that knowledge is available from various sources. Combined with the already strict quality control measures for aviation and military products, I am confident it is possible to deliver lead free soldered avionics products with sufficient quality and reliability. However, it will take a lot of effort from the suppliers.