What to use for logic control circuit without Programming?
Your bosses are not as out of touch as it would seem. Using a software approach to automation always has an issue: it’s not self-documenting, at least, not in the way that a logic or relay diagram is. This makes the system more difficult to analyze.
A Silego Greenpak could do this logic-oriented approach, for very cheap. It uses LUTs to implement gates so you could render the logic more or less directly. Uses a GUI for design entry, dev environment is very affordable. And it’s self-documenting.
More conventional ways to implement logic include a CPLD or an FPGA. You need to ‘program’ these using some kind of hardware description language like Verilog, but you could express your gate logic directly as your coding style and extract a schematic from that for your bosses to look at.
Really though this sounds like a job for a PLC, which solves a bunch of other problems too, like I/O conditioning. There are GUI front-ends for them that avoid ‘coding’ per se that model the kinds of behaviors that relays implement, so they are self-documenting to an extent (the very reason for ‘ladder logic’ is to solve that conundrum, making it possible for non-programmers to understand what is supposed to happen.)
Here’s a whole bunch of cheap PLCs, some under $50. https://www.allaboutcircuits.com/news/low-cost-programmable-logic-controllers-for-the-frugal-engineer/
And finally, PLC on Arduino is a thing. Worth a look.