Here is an excellent FAQ on preventing cross pollination in tomatoes.

You are correct that any cross pollination in the first year would only affect the seeds, not the fruit.

Rodney

Agree. If you aren't planning on saving the seeds from the Krims then there is no issue. If you do want to save seeds from it then you will need to bag some of the blooms and save seeds from those fruit.

Dave

while it's possible for cross pollination, it is rare in tomatoes since they self pollinate extremely easy.. by the time the blossom opens, it typically is already pollinated.

Usually, most of the time, but not always, Stevie. I've gotten a few different tomato varieties in trades in recent years that were definitely not true to type. It's frustrating when you wait months for something to produce only to find out it isn't what you wanted.

Rodney

Agree. There should be a forum that people list varieties and sources of crossed varieties. I give the name "Corrupt" in my seed inventory and just looking over seed packs with that label:

Black Krim

Big Rainbow

Stupice

Brown Berry

the list is far more extensive than I care for and these are all purchased seeds.

In my limited experience, saving seeds w/out bagging I have not observed any cross. I gather that tomato cross pollination is very low if not rare unless there are heavy insects activit, plants are very close and you get a lot of wind.

A flower's own pollen is right there, next to the stigma and have many times higher chance to self pollinate, before the birds and bees wake up and come along lingering. hehe

sey