Would you start anticoagulation in a patient with RCC and related (tumor) thrombus with extension to renal vein and further?  

Tumor thrombus is an intraluminal extension of tumor mass, rather than a true thrombus. There is no evidence that anticoagulation improves outcomes in tumor thrombus (Marcoux et al., Blood 2019). Primary management is surgical resection, typically as part of radical nephrectomy for localized RCC or ...

If it's radiographically read as tumor thrombus (not always easy), no AC. If bland thrombus component, AC.

Tumor thrombus usually can be distinguished from bland thrombus by contrast enhancement, vessel expansion, and PET scan activity. If clearly bland thrombus, I will AC and avoid IVC filter.