Glossary entry (derived from question below)
French term or phrase:
Sensible à (here)
English translation:
aware of the need to
French term
United Kingdom
www.lingocraft.co.uk
Native in: English (Variants: British, Scottish, Irish, Singaporean, UK, South African) 
Works in: French to English, Italian to English, Romanian to English, and 2 more.
Sensible à (here)
"Sensible à la protection de l’environnement et des animaux, xxx s’engage aussi à offrir des soins Vegan et Eco Friendly, non testés sur les animaux."
Non-PRO (2): Jennifer White, Rachel Fell
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Proposed translations
France
FR/AR-EN, broad range of domains
Native in: English 
Works in: French to English, Arabic to English, Italian to English
aware of the need to
envionmentally aware/Conscious of / aware of/concerned with/sensitive to
France
Wine, literature, tourism
Native in: English (Variants: British, Irish)
Works in: French to English, English
Attentive to
Germany
An American scholar based in Germany
Native in: English (Variant: US)
Works in: French to English, German to English, English
environmentally conscious
https://www.entitymag.com/start-environmentally-conscious-be...
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Note added at 2 hrs (2018-04-04 20:15:07 GMT)
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If you want to keep "the protection... ," then "dedicated to the protection of the environment/wildlife/... " should be fine.
sensitive to ....
1. adjective
If you are sensitive to other people's needs, problems, or feelings, you show understanding and awareness of them.
[approval]
The classroom teacher must be sensitive to a child's needs. [+ to]
He was always so sensitive and caring.
Synonyms: thoughtful, kind, understanding, feeling
https://www.collinsdictionary.com/dictionary/english/sensiti...
Synonyms of 'sensitive'
Adjective
1 thoughtful, kind, understanding
He was always so sensitive and caring.
thoughtful a thoughtful and caring man
kind He was a very kind man, full of common sense.
understanding Her boss, who was very understanding, gave her time off.
feeling He is a very warm and feeling person.
kindly He was a stern critic but an extremely kindly man.
concerned
patient
responsive
intuitive
receptive The patient was not at all receptive to treatment.
attentive At parties he is always attentive to his wife.
perceptive
considerate I think he's the most charming, considerate man I've ever met.
tactful I decided it wouldn't be tactful to order another beer.
unselfish
https://www.collinsdictionary.com/dictionary/english-thesaur...
Devoted to / dedicated to
To me, 'sensitive to,' 'aware of,' and other things along those lines make it sound like the company has heard of the importance of protecting animals and environment, but without being particularly moved by it.
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