The text you are being asked to sign these days about banning conversion therapies in the European Union is not just one more petition: it is a European Citizens' Initiative, which is far more potent and relevant.
https://eci.ec.europa.eu/043/public/#/screen/home
A European Citizens' Initiative is an instrument defined in the European Constitution, allowing citizens to submit a law or amendment to an existing law to the European Commission and the European Parliament.
Concretely, this means that if the Initiative succeeds, the legislative proposal will be examined by the Commission and submitted to the Parliament by the committee that launched it.
The European Citizens' Initiative system has existed since 2012. It is a relatively rarely used system, notably because it is rather demanding: the committee that authors the Initiative must comprise citizens from at least 7 Member-States, the Initiative must not infringe on the values of the European Union, etc. Since 2012, only a few dozen European Citizens' Initiatives have been attempted, and only 7 of these have succeeded in gathering the required number of signatures. Should the Initiative banning conversion therapies succeed, it would be the eighth to do so.
And after that, what next? Quite honestly, the European Commission could very well decided to answer "thank you, we don't care". This happened in 2014 after an anti-abortion Initiative, the "One of Us" Initiative, managed to gather the required signatures (shame!), and both the Commission and the Parliament politely declined to follow suit.
But the very same institutions can decide upon examination that, indeed, the question of the Initiative warrants modifying the law. For instance, the proposals from an Initiative against animal suffering, which succeeded in 2018, are currently being integrated into European law.
The European Citizens' Initiative is not without its weaknesses, but allows European citizens to bring proposals to their lawmakers, and thus to improve the law.
Anyhow, if you're a citizen of any country in the EU, do sign the Initiative!