I don't think it is possible to turn of weapon ranges entirely, but it is very easy to give every weapon in the game more range than the map size. You may have to contend with a bit more lag since the firing calculations for every ship would be up the wazoo, and ship behaviour may be erratic as well.
Nevertheless, the change is quick and easy.
Here it is:
The vanilla weapon data is held in a single file; weapons.csv.
A csv file is a comma seperated file that can be opened with (recommended) spreadsheet software, or even (not recommended) a simple text editor.
I am on mobile but the file ahould be found in starsector/starsector core/data/weapons/weapons.csv.
Make a copy of this file before working with it.
In this file there will be a column named range. Simply add a few zeroes to the end of the numbers in that column to give weapons a practically infinite range.
Do keep in mind for projectile weapons, the speed of the projectile is seperate. Meaning that (nearly) instantaneous weapons like beams will be dominant if you make this change. And ballistic or projectile weapons will take a back seat if you don't change the projectile speed (also found in the same file near the far right side).
Keep in mind that you may also have to change the projectile life time for missiles if you don't want them running out of fuel halfway. The range for missiles only determines how far the ai will shoot it from. Not whether it would reach the targeted ship.
Edit: Mobile spelling.
+ backup addition.
Edit 2:
On second thought, maybe haphazardly increasing the range on weapons isn't a good idea. The game has to keep track of projectiles, and if projectiles last forever off screen, the memory overhead is going to be immense. I'd recommender maybe increasing ranges to the 8000-1000 range instead of any magnitutdes bigger than that. It won't reach from end to end of the map. But it will reach up to the middle.
Anyways. Give these values a test and increase if you want.