I do not think that the claim can be confirmed or denied. The video is originally a Tik Tok posted as a comment reply to this user's Instagram. The claim is that as of right now, you may not declare yourself from Palestine should you be living in Canada. The creator is upset that an entire country and the identity is being wiped.
The video seems really convincing and I think it is accurate, but there are a few things to unpack.
https://palestinegd.ca/driver-license
According to this website: There is a system in place to use and renew a Palestinian license with no specific restrictions that it lists.
https://irb-cisr.gc.ca/en/country-information/rir/Pages/index.aspx?doc=458729&wbdisable=true
To this source, what I can gather is that Canada doesn't recognize Palestine as a state until Israel does. I am not sure to what political reasoning there is behind this if there is any, but I am not sure it has to deal with the conflict directly.
https://www.international.gc.ca/world-monde/international_relations-relations_internationales/mena-moan/israeli-palestinian_policy-politique_israelo-palestinien.aspx?lang=eng
This source shows they have support and recognition of both sides, and I cant quite understand if it has any side in the taking away from Palestine as a state.
https://www.aljazeera.com/news/longform/2023/12/2/israel-palestine-and-canadas-schizophrenic-foreign-policy
Lastly this source explains that Canada hopes to tread a middle ground tot the conflict, which really tells me that the drivers license issue doesn't have any stake in being a statement but rather just a recognition policy. I find it hard to believe the outward opinion of their government would intentionally misalign with their own Driver's License/ Identification program.
This is a very heated topic so a lot of sources covered the main issue, but not all credible ones, and also not this specific topic regarding the drop down menu, it also seems like it may contain a lot of author speculation.
As to people not being from Palestine in Canada:
https://www.canada.ca/en/immigration-refugees-citizenship/news/2023/12/immigration-measures-to-help-people-affected-by-the-israelhamas-conflict.html
They recognize the conflict and this seems to say that there are options to migrate from people affected by the conflict, but there is a visa limit and a certain amount of relation necessary to be allowed into Canada.
Overall if anyone can find anything directly from the Driver's License menu issue please comment the way to find out.