Take the random sentence "Start with the basics." Would you pronounce both "th" sounds separately or link them essentially saying "withe". Being a non native speaker I find pronouncing both difficult without disrupting the "flow of speech" which is often stated as being very important when speaking english.
I think it depends on the region whether or not someone will say both "th" sounds or not. I'm American and from the Pacific Northwest, and I tend to merge the two words into sounding like this:
Start wi-thuh basics.
As with most languages (I'm sure), people are lazy, and sounds will tend to mesh together if they're similar enough. But as I said, it probably depends on who you ask whether or not those words are said separately or not.