The MacBook Pro (Retina, 13-inch, Late 2013) has an Intel Iris 5100 GPU and is capable of supporting an HDMI-compatible device, including 4K, while using one Thunderbolt display or it can support two Thunderbolt displays.
In terms of external resolution, this model supports up to 3840 x 2160 pixels at 30Hz or 4096 x 2160 pixels at 24Hz (using HDMI) or up to 3840 x 2160 pixels at 30Hz (using Thunderbolt).
According to the specs of the Acer R241Y, this has a maximum resolution of 1920 x 1080 at 60Hz. And, according to the user manual, this resolution is achieved using VESA mode.
On your MacBook Pro:
- REFRESH RATE - As a first step, I would check the Refresh Rate set in your MBP. You can find this under the Display tab within System Preferences > Displays. If you change it, you may need to wait a couple of minutes to ensure the change has taken effect properly.
- RESOLUTION - I would also double-check you're not using the Scaled option for your resolution. Instead, make sure you have the Best for display option selected - also found in System Preferences > Displays.
- RESET NVRAM - It may be worth resetting your NVRAM. If you're unsure how to do this, refer to my answer here. Make sure you look under the PRAM/NVRAM heading.
NOTE: If, at any point, the display switches off after configuring options in your Displays System Preference, just press the Esc key to undo the last change.
- On your Acer R241Y display:
If you're still having issues after checking/trying each of the above, try the following:
- Mode type - If your display is already in Auto mode, manually try each of the others (e.g. Standard mode, Graphic mode, etc) one by one. If it's already on a specific mode, then try it in Auto mode instead.
- Focus - You can also manually configure the display's focus. You should be able to do this by going to the Picture Menu.
- Reset your display - There should also be a Reset option on your display's menu. It may be worth trying this if all else fails.
Since your issue is around how fonts look, there is also a setting in your System Preferences > General. Maybe try ticking/unticking the Use LCD font smoothing when available option to see what difference that makes.