Unfortunately it doesn't, because they're literally identical analogies and you're saying that they're different. Lets try swapping Christian & Mormon/Hindu beliefs in your explanation:
Abortion is against my religion
(Consuming coffee/tea & beef is against Mormon/Hindu religion)
Some of my tax dollars are given to Planned Parenthood to fund abortions
(Some of Mormon/Hindu followers tax dollars are given to SNAP to fund the consumption of beef & coffee/tea)
That is forcing me and other Christians to participate in this act, against our will and religious beliefs
(That is forcing Mormons/Hindus to participate in this act, against their will and religious beliefs)
Mormons are not being forced to drink tea and coffee against their will...
And those who practice Hinduism are not being force-fed cow meat....
(Those who are Christians are not being forced to have abortions...)
What they consume is a choice they can make. I have no choice but to fund abortions.
(Not getting an abortion is a choice Christians can make. Mormon/Hindu followers have no choice but to fund the consumption of beef & coffee/tea.)