The typical way we handle this case where your output device is active-high, and can't tolerate the glitch, is to put a *stronger* external pulldown on the lO line.
Typically the internal pullups are pretty weak, in the 80-150K range -
The pullup value is usually given in the datasheet, but its not listed in the ESP-8266 summary datasheet that i found.
However they do mention a "hold" function that requires 5uA to override, and that GPIO maximum output current is 12mA ;
So a pulldown current of up to ~ 1-2mA would be safe to use - i.e. in the ballpark of 3.3kohm @3.3V should do the trick.
Putting large capacitors on IO lines is not generally not recommended, as this can cause high peak currents on those IO when they switch, make edge rates very slow, and cause EMI / latchup issues later on -
so not good for reliability