I usually say yes! I have always believed in interlining with competition so that can't stop me. What can stop me is cost. If I fly a few flights to a place and the IL costs over 100k its way cheaper just dropping the flight. Though you never want to make enemies so just send a nice letter saying why you cant interline at the moment but you are of course open to future collaboration. Others who I usually won't interline directly are with new airlines who I don't believe will make it. If the IL makes sense I will just wait a month or two and then sign it. Or depending on the size of a market and the personal relation to a partner I won't IL with his competition. If I have a good friend in the EU I probably won't IL with his competition out of respect. Though if I don't know the people I would try to IL with everyone in a market. Alliances might also have exclusivity agreements which cant be broken!
One rule, never cancel an IL if not out of extreme desperation! For me, it was extremely rude when players canceled as I had to change schedules and slots were usually tight.