Praise be to Allah
If the projects that the company undertakes are permissible projects, and the programmer asked about does not directly deal with the finances of the company, as you said, then it is permissible for him to work with that company, but it is better for him to look for other work, because it is makrooh to work with those who deal with riba.
The sin of riba is borne by the company and those who directly deal with riba or help with it, or approve of it. As for the salary of the programmer, he has received it in return for permissible work.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked about an employee who works for a company that deals with banks and takes out riba-based loans from them, and gives the employees their salaries from those riba-based loans.
He replied: Does this employee write the contracts between the company and the banks?
Questioner: He does not write them; rather it is me, O Shaykh! (i.e., he is the employee about whom the question is being asked).
Shaykh: Then you do not write down the riba-based contract, you do not witness it, and you do not take or give riba, so I do not see anything wrong with this, so long as the work you do for the company is sound (and free of any haraam element), in which case the burden of sin is borne by the company itself. If you do not go to the bank or sign any transaction with the bank, then there is no sin on you. This company – first of all – was not established for the purpose of dealing in riba, and it is not like the bank concerning which we would tell you not to take a job there. It was not established for the purpose of dealing in riba. Secondly, you are not dealing directly with the riba, by writing it down, witnessing it or offering any other service connected to it; your work is separate from the riba.
End quote from al-Baab al-Maftooh (59/15).
And Allah knows best.