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i.e. <h1 style="margin: 0px 0px 0px 30px; color:White; font-size:24px;">TextText</h1>
I think the value is diluted. Please correct me if I am wrong.
CSS is today mostly ignored by spiders (and external CSS are typically not even touched at all), but such things can change or can be evaluated manually regardless.
If you drop table layout n favor of CSS, you should see a decrease of the total size of the html (significant decrease), and that would yield nothing but good (keyword density, simplicity to parse, load time, ...).
But SEO isn't the main driver to get CSS.
the value(importance) of the h1 tag is diminished because of the css style within the actual tag
By value I assume you mean "TextText" in your initial example. Therefore I fail to see how any style on this element can have any effect on the importance of the value itself, in terms of search engines, if that is what you mean? I don't think the OP is refering to 'diluting the style'? (IMHO)
However, it is technically possible that if an intelligent robot could determine that your 'white' heading was on a 'white' background (ie. not visible to those viewing the page) then it could be considered as trying to spam your keywords and have a detrimental in the SERPs - IMHO.
(EDIT: I should refresh the page - I see swa66 got there before me! :)