This is a great question without a clear answer. People have struggled to find the answer since the 1970s:
Here is my 2002 paper with many references listed in Appendix A. See also my dissertation on the topic.
There are many cases of two languages or two dialects with the same or similar phonological inventories (the same phonemes), which substitute different sounds in place of /θ/, usually either [t, f, s]. The consonant [t] appears to be the most frequent substitute, and this is usually attributed to it being the "unmarked" consonant (most frequent cross-linguistically, easy to articulate).
Researchers have proposed many different solutions, but as far as I know, there is little consensus. Some have proposed that different dialects have different grammars (e.g. Weinberger 1988, Brown 1998, Lombardi 2003). Others say that it depends on "functional load" (e.g. Hancin-Bhatt 1994): The functional load of a given feature value (e.g. +continuant) is equivalent to the number of times it is specified in the phonemic inventory divided by the total number of phonemes. Note that this approach does not account for different substitutions in two dialects with the same phonemic inventory (e.g. France French [s] vs. Québec French [t]).
Still others say that it is not the phonemic inventory that is important, but instead it is the phonetic implementation that matters (e.g. Brannen 2002, 2011). For example, the actual pronunciation of /t/ can be different from one dialect to another, e.g. English has an alveolar /t/, but many languages have a dental /t/ (closer to the place of articulation of [θ] which would make dental [t] a good substitute.)
One thing that is clear from the research however is that this is not simply a production phenomenon: speakers of languages that do not have [θ] misperceive this sound differently, and it depends on their native language.
Brown, C. (1998). The role of the L1 grammar in the L2 acquisition of segmental structure. Second Language Research , 14, 136-193.
Hancin-Bhatt, B. (1994b). Segment transfer: A consequence of a dynamic system. Second Language Research , 10 (3), 241-269.
Lombardi, L. (2003). Second language data and constraints on Manner: Explaining substitutions for the English. Second Language Research , 19 (3), 225-250.
Weinberger, S. H. (1988). Theoretical Foundations of Second Language Phonology. PhD Dissertation . University of Washington.