I know it is bad to solder lead-free devices, such as resistors, with lead. However, is it possible (with less effort) to remove this lead-free coating on the resistors to make it possible to solder with lead? PCB has also a chemical coating.
The coating on the leads is typically tin.
For Pb-free components, the manufacturer will have used Pb-free Sn, for example the datasheet for some resistors I picked at random says:
Pure tin plating provides compatibility with lead (Pb)-free and lead containing soldering processes.
Presumably by "solder with lead" you mean solder with tin/lead solder (e.g. 60/40 or 63/37). There will be no need to remove the coating.
There are many resistors out there which have lead free terminals, you just have to search in mouser ticking the ROHS compliant.
The problem of using leaded + unleaded solder is that the melting point can go down dramatically, in some cases below water boiling point creating reliability issues, however these days most components have pure tin contacts, and pure tin + leaded shouldn't pose a problem the same way pure tin + unleaded shouldnt.
YET... there is more to the story, because it's not only the terminals that may contain lead, also the ceramic substrate of the resistor. You can tell which have leaded ceramic as in the ROHS certificate it says compliant by exception.
This won't affect the performance of the circuit however for environmental consciousness you may want to avoid them if the specs allow you to.
There are options without leaded ceramic such as RC0603FR series, i guess more will pop up in the future