Can't play FIFA 17 online and FUT

You may wish to look here - https://www.fifauteam.com/fifa-18-carryover-transfer-guide/ This is how EA have chosen to impliment the game, and not Microsofts.

You didn't say what FIFA version you were using on the 360 but I think one of these applies.

Same Platforms, from FUT 17 to FUT 18 or from FUT 18 to FUT 18

• 
  From XBox 360 to XBox One (FUT 17 -> FUT 18)
  
  From XBox 360 to XBox One (FUT 18 -> FUT 18)
  
  You no longer can share your stuff between different consoles, even if you are still playing on the same platform. This means coins, club items and transfer market items will no longer be shared between Xbox 360 and Xbox One, and between PS3 and PS4. You’ll
  only keep what’s linked to your Origin account. That is your XP and FCC.

Hey, TAPPY71! According to
EA's Edition information for FIFA 17, you received exactly what you should have on the first sign in. You will want to sign in to FUT each week for 4 weeks to get your weekly draft token. You would only receive the FUT Kit if you pre-ordered, based on the
same article.

If you have any issues with getting your future draft tokens, you will need to reach out to EA for further assistance. Thanks for understanding!

Maybe a stupid question, but did you redeem the online pass?

You need to redeem your online fifa 13 pass to make the online part of FUT (Fifa Ultimate Team) to work.

Hey ReverPlayer -

Sorry to hear about the issue. According to EA's information page on
what's included with copies of FIFA 17, you should receive your items once you enter FUT. While you check there, could you also let us know what exactly you're supposed to receive with the code you redeemed? We want to be sure we're looking in the right
place for your items.

Keep us in the loop!

Hi Birnenkopf,

It sounds like the issue is because you're combining streaming with playing an online game and something there is conflicting, causing the drop-out.

Does this happen with multiplayer in other games too for you, or is it limited to FIFA 16? What about other online modes in FIFA 16, do they also fail or only FUT presents this issue?

Try to not play too many multiplayer games to test this, as it might negatively impact your disconnection rating within FIFA, but I'd be interested to know if this problem is limited to FUT or other modes and games give the same errors.