Using Dark Mode Everywhere mod also darkens the Xaero's Minimap mod. Is there any way to stop it from affecting Xaero's Minimap?

Yes, there is, but it's a bit contrived - it involves the shader method blacklist in the mod config.

And how can we do that please?

it's not trivial to explain 😓 take a look at the README on curseforge/modrinth and see if you can crack it.

I think if you actually look in the config file/menu there are comments/tooltips that try to explain how the options can be used to blacklist certain UI elements.

For forge 1.20.1, adding these to the shader blacklist seems to do the trick:
xaero.common.minimap.render.MinimapRenderer:renderMinimap
xaero.common.graphics.GuiHelper:innerBlit