I'm sure this has probably been brought up many times but I've just recently started using hcrealms again so I'm not sure but can someone help me out. If

If I use a theme team, and my opponent and I both play a BFC. Can I choose to ignore my own if I think it will hurt my opponent more than me. For instance if I play "poor teamwork" and ignore my own BFC, would it then only affect my opponent and allow me to still carry and TK friendly figs?

Yes, you may choose to ignore your own BFC, your opponent's BFC, or nothing at all (nothing says you have to use your Ignore).