It didn't mix so far in UK - it does in many other countries with different kind of political systems. The centre right of the Tory party, and the centre left of labour- has a lot more in common than the extremes of each. ERJ has more in common with the UDP and Ukip...
And for voting- for now- revoking art 50 or getting a peoples' vote- is more important than anything else. They'd be voting tactically of course. I believe they all want a decent education system, to save the NHS from privatisation, to deal with the environment and pollution, effective international research and innovation, etc, etc, etc.
The old 2 party system is broken and not fit for the challenges of the 21st century - onwards and forwards to the future- strong in the EU and ready for reform, at the top table.