Will taxi drivers understand where I'm going?

If you use Grab or Bolt, yes, because the driver follows the GPS. If hailing a street taxi, always confirm they use the 'Meter' before getting in, and use a map app to show your route.

Is it rude to not speak Thai?

Not at all. Locals are accustomed to tourists. A simple 'Sawadee-krap' (male) or 'Sawadee-ka' (female) as a greeting is appreciated, but not required.

Bangkok navigieren ohne Thai-Kenntnisse

You don't need Thai to get around Bangkok because English is widely spoken in tourist areas and major transit hubs. Download Google Maps, use the Grab or Bolt apps for transport, and always keep your hotel's address saved in both English and Thai on your phone.

Get a local SIM card. Purchase a tourist SIM (AIS or TrueMove) at Suvarnabhumi or Don Mueang airport. It costs about $10 for 8-10 days of unlimited data. Do not rely on hotel Wi-Fi alone.
Use ride-hailing apps. Download Grab and Bolt before you arrive. These apps show the price upfront and provide GPS tracking, eliminating the need to explain your destination or negotiate fares with taxi drivers.
Master the public transit. Use the BTS Skytrain and MRT Subway. Signage and ticket machines are bilingual (Thai/English), and announcements are made in both languages. Use a Rabbit Card for the BTS to avoid ticket queues.
Carry an 'Emergency Card'. Ask your hotel front desk to write their address and phone number in Thai on a business card. If you get lost or need to take a taxi, show this card to the driver.

Will taxi drivers understand where I'm going?: If you use Grab or Bolt, yes, because the driver follows the GPS. If hailing a street taxi, always confirm they use the 'Meter' before getting in, and use a map app to show your route.
Is it rude to not speak Thai?: Not at all. Locals are accustomed to tourists. A simple 'Sawadee-krap' (male) or 'Sawadee-ka' (female) as a greeting is appreciated, but not required.