Depth of Downtime
Pay attention to the amount of real-world time you spend in downtime and the level of detail. Downtime should rarely last a whole session. Usually, a half hour between significant adventures is about right, and 15 minutes for shorter lulls in the action, such as when PCs return to a port of call briefly in the middle of an adventure. You can extend this time as needed for more detailed roleplaying scenes.
For the level of detail, it's important to give more than just an overview, but often the basics will do. “A fleet of ships await boarding clearance, and a uniformed vesk officer puts you to work double-checking manifests” might do for using Piloting to Earn Income, and “Your shipment of UPBs arrives late, but you're able to complete the armor” could be enough for Crafting. Go deeper if the player sets out to do something specific or asks questions you think have potential for an interesting story, but be careful with too much detail, as you run the risk of boring most of the table with minutiae.
Group Engagement
If a player really isn't interested in downtime, they might not want to engage at all. In that case, it's best to shorten the time you spend on downtime and give their actions a one-sentence description. If other players want a deeper downtime experience, consider extending game sessions or running side sessions for just those players.
Campaigns without Downtime
In the second, you and the other players just don't care about downtime at all. It doesn't interest you. In this case, just summarize what happens between adventures and skip using any downtime rules.
If you skip downtime, you might not need to adjust your game. The money PCs can earn during downtime is minor compared to what they can gain through adventures. However, the PCs will have less choice in what items they get if they don't Craft or earn extra money to buy items.