There are several types of bindweed and they are not even related which is an excellent example of how to start to make sense of conflicts:
So the first thing to do is always establish which LATIN name they are referring to - rather than which COMMON name. You may find that they are talking about two different plants!
With bindweed there are two main genera/species involved:
Hedge (or climbing) bindweed and Field (or smaller) Bindweed.
the first is Calystegia sepium and the second is Convolvulus arvensis. These are both at a higher level (genera) Convolvuleae.
Beware there is another type of 'bindweed' that you see sold as a decorative garden plant (often in blue) called commonly 'Morning Glory' whose Latin name is Ipomoea (or was until recently - but lets not bother with recent re-classifications). This latter is a member of the Ipomoeae rather than the Convolvuleae -
although at a higher level still (Families) they are all related.
NOW . . . you will see immediately that anyone just referring to 'Bindweed' in a forage book without telling you which bindweed (by using the Latin name) is already causing a muddle by conflating at least three different plants.(and the same is true of using terms like 'daisy' etc).
Having established WHICH bindweed you are talking about you can either rely on the person whose book/article appears to know what they are talking about by differentiating these things - or enquire at greater detail as to whether the book/article justifies or describes why they feel they are/are't 'toxic' (a term much bandied about which should always be defined), and which parts.
If we return to 'Bindweed':
Experience with MICE (not rabbits who have never been tested and may not react in the same way at all) show the the Convoluvulus arvensis can cause long term organ damage if fed as a substantial part of the diet over long periods. This may or may not be relevant to rabbits (Frances harcourt Brown believes rabbits have excellent internal protections which many other mammals with different methods of food ingestion do not).
HUMANS have been shown to react to both of the other types (and most particularly the Hedge Bindweed) as a laxative or purgatives (most particularly the SEEDS) - again no direct testing on rabbits who rarely appear to get this sort of side effect due to their method of hind gut digestion etc.
In addition HUMANS put about a rumour in the 1970s that smoking the seeds of the Ipomeae gave halucinogenic side effects . . . although one can be fairly certain that your rabbits are not going to smoke the seeds! This has been the cause of MUCH confusion in books as people just equate Morning Glory with 'bindweed' and think the seeds are 'toxic' (short hand for having a possibly unpleasant side effect)
One last caution remains - that the entire genera are sometimes apparently more susceptible than some other plants to the ergot fungus that can also infest ryes etc in damp weathers and cause the typical ergot toxic effects in humans and animals. However that is not inherent in the plant itself and any plant that has thi would probably be distinguishable and avoided by a rabbit who has an incredible sense of smell.
So . . .
there is no one 'bindweed';
there are no studies of any of the bindweeds on rabbits
studies that have been done suggest that the vegetation of Field Bindweed may have an effect on internal organs of another small mammal - and I have therefore put a 'rider' on my recommendation of it in my book
Most Convulacea have a possibly laxative effect in humans - possibly through the seeds but you are probably not feeding the seeds to your buns and they have a different food processing mechanism anyway -
The motto is - make sure the book or article you are using specifies WHICH plant, WHAT toxins, WHICH studies (if any), . . . and never let your rabbits smoke Morning Glory . . .