Hi,
I believe this is not a CSS issue in this case, as all the range slider CSS classes are prefixed and have a specificity to only apply on the search settings box an nothing else whatsoever.
It is however possible, that the NoUI slider script versions are different, and they override each other. It is however possible to turn off the slider script within Ajax Search Pro, so that the conflict should go away. One the Compatibility & Other settings submenu, open the CSS&JS loading options panel, and turn off this option: https://i.imgur.com/aznlPAt.png
After that, make sure to clear your site & browser cache. This should solve the issue.
