Is it permissible to subscribe to programs that support homosexuals, such as Adobe, for use in one's work? And does that justify downloading them for free to avoid supporting forbidden things?

It is permissible to subscribe to and benefit from permissible programs, unless they involve assisting in something forbidden. The corruption of the owners of the company producing the programs or their open declaration of indecencies does not render it forbidden to deal with them through buying and selling, unless it involves assisting in their disbelief or immorality.