The Wikipedia entry for Ion states "A positively charged hydrogen ion (or proton) can readily combine with other particles and therefore is only seen isolated when it is in a gaseous state or a nearly particle-free space." Cells pumping ions across membranes is very common so can someone help me understand what context might be implied by the quote?
I'm still not entirely sure what specifically you're asking about, but I have a guess. It is true that positively-charged hydrogen ions, or bare protons, are typically only observed in gaseous/plasma states and hard vacuums, and it is also true that cells routinely pump positively-charged hydrogen ions across membranes. This is not a paradox because in aqueous solutions, hydrogen ions exist as $H_3O^+$, also known as hydronium or hydroxonium.
Image from Wikimedia Commons
You are on the right track with your thinking about the paradox of an actual proton being pumped across the membrane, and it's just a problem of how the chemistry is communicated. The protons actually move along what is called the proton channel, which essentially is a row of protonated amino acids like glutamate (glutamic acid) or histidine.
If we think about complex 1 in mitochondria (below), when a proton in the matrix is "pumped" across, it actually "pushes" protons down the proton channel into the matrix (See the light blue line in the figure below). Think of a series of train cars on a track getting pushed.
Finding these proton channels and figuring out how they work is actually a very competitive field. Since they are buried in the membrane, they are challenging to work with, and we don't know much about them.
Even as someone who works in the field, I have to remind myself that all chemistry works this way. If it is water, protons, or electrons, talking about a single molecule is the wrong way of thinking about it.
Citation for Figure https://www.nature.com/articles/s41467-020-17957-0