Ideologies should have overlap.

For both historical flavour and game improvement, I'd like it if each pair of ideologies had two or three shared tenets that get kept if you switch between the two. It would give a lot more leeway if you're an early founder with an influential rival yet to declare, and make a lot more sense - why would a socialist revolution switching England to Order scrap the NHS?

Here's my suggestions:

All: Universal Healthcare.

Order-Freedom:

Social Democracy (new; halves unhappiness for rivals' influence), Skyscrapers (added to Freedom), Avant Garde (overwrites Hero of the People).

To fill the imbalance, Order gains Full Employment: Unemployed citizens generate +1 gold.

Order-Autocracy:

One Party State (new; reduces rivals' cultural influence by 33%), United Front (added to Order), Young Pioneers (added to Autocracy).

Freedom-Autocracy:
Welfare State (new; adds +0.5(?) happiness per unemployed citizen), Capitalism (added to Autocracy), Elite Forces (added to Freedom).

To some degree, it already supports this. You get a full refund of all policies chosen in the old ideology other than free ones and you are free to immediately pick Universal Healthcare again.

Ideologies already overlap by sharing 2 of these 3: military, science and diplomacy.

I agree, Government types should also be added to the game, then it would look like.

Incan Socialist Autocratic Monarchy

Civilization 5 makes ideologies act like government type but really ideology should be inside government and social policies should be inside ideology.