While there could be other motivations involved, my answer will focus on the security-related reasons in postponing the State of the Union. Other motivations not publicly stated are speculative.
In Speaker Pelosi’s letter to President Trump, Pelosi cited that the Security of Homeland Security Kirstjen Nielsen designated State of the Union addresses as National Special Security Events and would require additional resources from the Federal Government to ensure security of such events.
This designation means that the Secret Service will be leading in developing and maintaining security operations.
The designation of the State of the Union under NSSEs means the Secret Service "becomes the lead federal agency in developing, exercising, and implementing security operations," according to a NSSE fact sheet from the Congressional Research Service.
Currently, the Department of Homeland Security, which the Secret Service falls under, is not funded and only essential employees continue to work. However, an official from the Secret Service did mention that they are ready to provide security for the event.
That has included most personnel responsible for planning security measures around the address, the official says. Meetings about the event have continued to take place during the shutdown. The official says security planning for the State of the Union began months ago, before the shutdown started.
With that said, there are also other federal agencies involved in providing security, such as the Capitol and Metro police forces. With a lack of funding, it could hinder their ability to plan and execute security measures for the event.
Because the State of the Union is a designated "National Special Security Event," it requires assets and support not just from the United States Secret Service but across multiple government agencies, including some closed by the shutdown, a separate law enforcement source told CNN. That could be difficult to plan and execute because of the lapse in funding, the source said.
So, while the government shutdown may not entirely prevent the State of the Union address from taking place, the planning and execution of security measures are indeed hindered. For more information, check out this CNN article.