Can my Belgian company ship spare parts to Turkey if the end user might be on an EU sanctions list?

No, you should not ship yet if the final end user is still unclear.
From an EU sanctions perspective, the main issue is not Turkey itself, but whether your goods could be made available, directly or indirectly, to a listed person or entity. That risk also extends to a non-listed company that is owned or controlled by a sanctioned party. So if your Turkish distributor cannot clearly identify the final customer and end user, that is already a serious compliance red flag.
Before shipment, you should require a proper due diligence file. At minimum, this should include the full identity of the final end user, company registration details, address, beneficial ownership information, exact end use of the spare parts, installation site, and a written undertaking from the distributor that the goods will not be resold, re-exported, or supplied to any other user without your prior written approval. The commercial documents must also match that story, including PO, invoice, transport route, and payment flow.
You should screen not only the distributor and declared end user, but also their UBOs, directors, and known affiliates against EU sanctions lists, and check whether there is any ownership or control link to a listed person. If the goods are dual-use, or could have a sensitive military or restricted end use, the analysis becomes stricter and a licensing issue may arise under EU export control rules as well.
In practical terms, the safe approach is this: pause the order until the end user and end use are fully verified. If the distributor refuses transparency, gives inconsistent explanations, or cannot support the transaction with clear documents, the shipment should not proceed. Once the file is complete and screening is clean, the transaction can be reassessed and documented before dispatch.