John Hall tried to bring in a load of sports under the Newcastle Utd umbrella, even the Le Mans Listers were painted black and white.

Both Bradford clubs in the Football League had been prominent in the Rugby League but converted to the round ball in the 1900s.

Some don’t even have a football section anymore-  eg ManU

I suspect there will be a few London clubs that just sneak into the post-1900 category.  Will check later but teams like Richmond, Blackheath, Corinthians etc will probably have doubled up.  More recent examples will be much harder to find I guess 

Ha! From Wiki:

Blackheath, along with Civil Service F.C., is one of the two clubs that can claim to be a founder member of both The Football Association and the Rugby Football Union.

Oops - not post 1900.  Ignore the above

I think man U were an actual football club in the 1900s

Blackheath split from the Football Association after the fourth meeting because the FA voted to get rid of "hacking" - the kicking of an opponent's shins if they had the ball.  The rules of rugby allowed it at the time.  Somewhat ironic that Blackheath then led the drive against hacking two years later when they sussed that, while Tom Browne and Flashy could not do THAT much damage, it was literally life-threatening to have some fifteen stone roast-beef-fed army officer try to smash a leg into pieces.  By then though they had peed off the Association to the extent that they never sought to come back.

Yes there has. Bradford I think.

Negative. Close though

Huddersfield? 

No, the close bit was that Bradford Park Avenue and Bradford Rugby were nearly part of the same club. However the creation of the football team actually led to a split in the club so I don't think both teams ever coexisted under the same banner

Manningham was a rugby club but switched to adopt soccer and changed its name to bradford city.

Bradford rugby club was distinct from City/manningham. Bradford park avenue was the football part of the club

Huddersfield Town was the Football League putting a spoke in rugby league’s wheel. The League was keen on stealing the peanut-huggers’ thunder By promising places in the League for clubs in rugby strongholds. Hence Udders, Hull City, and Leeds City (expelled and replaced by Utd). 

Manningham Rugby Club became Bradford City in 1903.  
 

Bradford Rugby Club voted to become Bradford (Park Avenue) in 1907. But the Kinder-coddlers there didn’t go with the move and formed Bradford Northern RFC. 

Exactly. Neither are a correct answer to the question

No.

Bristol Bears, Bristol City and Bristol Flyers are effectively owned by Steve Landsdown’s Bristol Sport Group, and the main two both play at Ashton Gate.

Manningham (rugby) definitely became City (football). It was the same legal entity. It very much therefore is a correct answer to the question, unless the question requires the club to have played both codes simultaneously, which faod it doesn’t.