Hereto dismissing an employee because you disliked their politics was straightforward provided you acted quickly (i.e. before acquisition of unfair dismissal rights). From 25th June that will no longer be the case and dismissing an employee for their politics will be protected, along with other discrimination protection, a day one right.
There may be room for manoeuvre in serious cases. For example, there is no inherent right to campaign for a political party at work and employees who create an intimidating or hostile environment are not likely to be protected. It may in some circumstances be realistic to dismiss for a substantial reason if an employee’s politics conflict directly with the philosophy of the organisation; but ultimately that will be for the courts to decide in each case.
Finally it may be worth noting that the protection is from unfair dismissal. Unlike other anti-discrimination legislation it does not (yet) apply to selection unless it can be shown to amount to a belief.