Hi,

Seem you didn't check documentation for Soledad theme here

1/ To import a demo, please check the guide here

Note: Make sure you go to Dashboard > Settings > Reading > and make the config look like this image

2/ To switch to another demo style - please do following steps here to do that:

a) Install & active plugin Customizer Reset & plugin Customizer Export/Import

b) Go to Appearance > Customize > click to button "Reset" at the top to reset all your customizer data to default.

c) Import demo style ( .dat file ) you want to import to your site - by do following ONLY Way: 2 in this guide - Way 2: Import Only customizer data

Note: 

- After switch to another demo, if you have the issues about menu items appears like on the image you sent, you need to go to Appearance > Menus > create/select a menu > scroll down to bottom > and check to "Primary Menu"

Best Regards,

PenciDesign