Is that a direct flight or connected? My experience so far has been with LH, so I have no idea how British Airways work, but with Lufthansa check-in is done online and once You print Your boarding pass You can drop Your luggage in drop-off points by Yourself. Nobody has ever looked at my passport or ID- the pic is more or less up to date there, at least, but even if it wasn't, as I said, nobody ever looked at it, mostly because all actions are done by passengers themselves now ...
The "fun part" might be if You have connecting flight and are travelling via Frankfurt Airport, cause they replaced all their equipment with full body scanners and You cannot fool them. If You will be presenting as female, plus judging from Your avatar picture, most probably the security personell will scan You as female and that will inevitably bring up "suspicious areas", so expect being pulled aside and patted down by female security staff. In my case I just politely and silently told her not to be surprised about stuff which she might find, because I am transsexual. To my knowledge FraPort is the only one which introduced those measures, so if You are not passing through it, just disregard the last passage
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