Thanks for this Carolyn, there is the option to opt out of contact like it says.
Reading that, and considering the General Data Protection Regulations and Data Protection Act 2018 I'm gonna say no on that.
Consent should be freely given, specific, informed and unambigous. You cannot harvest information through a petition for improving local railways.
The only part you've got right there is asking if you can contact people to update them on the state of the petition (I'd even argue considering they're signing a petition for rail improvements you don't need that) but to forceably opt them into further communications and further more diseminate their details amongst other elected representatives (you don't even clarify how far that goes it could be the ward councillors, it could even be a Lib Dem Councillor in the Highlands for god sake) is completely and utterly unacceptable and in anyway in the spirit of GDPR.
Going even deeper... "you submit this form, the Liberal Democrats, locally and nationally, may use information in it, including your political views,
to further our objectives,"
What on earth does that even mean? That could be literally anything determined by the party at any given moment. There is no way this form is compliant with GDPR.
The only place that data should be used for is the petition, there should be seperate tickboxes for it they want contact on specific matters outside of the railway petition from the Lib Dems and another tickbox for diseminating that information amongst other elected representatives they have to be physically checked and that should be the default.