It seems that counting your father as your dependent shouldn't, in itself, cause him to be ineligible for SNAP.
Eligibility requirements for SNAP can be found on this FNS page. There are upper limits on the "countable resources, such as a bank account" that the beneficiary's household may have, and on that household's income. (There are some other requirements, too.) From what I can tell from your question, your father shouldn't be part of your household for SNAP purposes, because:
Everyone who lives together and purchases and prepares meals together is grouped together as one household.
If you're transferring him money, I assume he's living and eating somewhere else, so it seems you are not part of his household.
According to the IRS's Publication 501, your father is not required to be part of your household for IRS purposes to be your dependent. The test to qualify is that a non-child dependent
Live with you all year as a member of your household, or
Be related to you in one of the ways listed under Relatives who do not have to live with you.
However, by the "Special rule for parent", you may be able to use your father as your qualifying person (dependent) to be able to file as "head of household", so long as you pay more than half their support, and "more than half the cost of keeping up a home that was the main home for the entire year for your father".
I don't know if in this case the IRS would consider your father "part of your household" or not. Even if the IRS considered your father part of your household based on the way you filed your taxes, I think it's possible, as the IRS and FNS are two different entities, that the definition of your father's household for SNAP purposes could be different from the IRS's.