Is it possible to use pins that are taken by a shield display for other functions? Specifically, I want to drive an IR LED (which I understand needs a certain type of pin) while using one of these
The ESP32 board has the SD0-SD3,CMD,CLK pins that you could access.
But seriously, you are always going to use up most pins with a Parallel TFT.
I suggest that you buy a regular Red SPI display. e.g. 128x128, 128x160, 240x320, 320x480
Supported by Bodmer. Gives you lots of spare GPIO pins.
When SPI is used sensibly it does not waste any MCU resources.
Put a little bit of text instead of having links on their own line; e.g.
drive an IR LED (which I understand needs a certain type of pin) while using one of these https://www.ebay.com.au/itm/193738906640 with one of these https://www.ebay.com.au/itm/153356511425