Interest rate traders/quants do not really talk about rho, as in the sensitivity of the Black Scholes price to $r$. The reason, I guess, being that we use Black (not Black-Scholes) formula for options on forwards and there is no $r$ in that formula except in the discounting factor multiplying the undiscounted option value. Rho in interest rate models is then closely associated with the so-called "discounting risk" which is the sensitivity of prices to the curve you use for discounting. In the multi-curve world we live in it is typically calculated separately from risk to other curves (like Libor) and may, or may not, be aggregated with other sensitivities to the same curve.
Theta is a whole different story and it can get very complicated. A standard base-level definition of Theta in interest rates models keeps the forward curve constant when moving time forward. Almost by definition that means that you should keep the forward rate that goes into the Black formula constant when calculating Theta, so the time change only affects time value of the option. Traders do want to look at "other" thetas (and often give them other names such as rolldown, carry etc) such as when the spot curve is kept constant, etc. also it needs to be defined exactly which volatilities or, indeed, volatility smiles should be kept constant when calculating theta.